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# List of Mathematical Symbols

## List of Mathematical Symbols

This section lists the mathematical symbols that are used in Technical Studies Reference.

### Common Mathematical Operations

This section lists and explains some of the mathematical operations that are frequently used in technical studies.

#### Ceiling Function

The ceiling function returns the least integer that is greater than a given number. The notation for the ceiling function of a number \(X\) is \(\lceil X \rceil\).

Example: \(\lceil 3.3 \rceil = 4\)

#### Floor Function

The floor function returns the greatest integer that is less than a given number. The notation for the floor function of a number \(X\) is \(\lfloor X \rfloor\).

Example: \(\lfloor 5.8 \rfloor = 5\)

#### Moving Maximum

This operation returns the maximum of a set of values in a moving window of Length \(n\). Our notation for the Moving Maximum of a Random Variable \(X\) at Index \(t\) is \(\max_t(X,n)\), and it is calculated as follows.

\(\max_t(X,n) = \max\{X_{t - n + 1}, X_{t - n + 2},...,X_t\}\)In the event that there are not yet \(n\) values in the moving window (that is, \(t < n - 1\)), the Moving Maximum is calculated as follows.

\(\max_t(X,n) = \max\{X_0, X_1,...,X_t\}\)#### Moving Minimum

This operation returns the minimum of a set of values in a moving window of Length \(n\). Our notation for the Moving Minimum of a Random Variable \(X\) at Index \(t\) is \(\min_t(X,n)\), and it is calculated as follows.

\(\min_t(X,n) = \min\{X_{t - n + 1}, X_{t - n + 2},...,X_t\}\)In the event that there are not yet \(n\) values in the moving window (that is, \(t < n - 1\)), the Moving Minimum is calculated as follows.

\(\min_t(X,n) = \min\{X_0, X_1,...,X_t\}\)#### Moving Range

This operation returns the difference of the Moving Maximum of a Random Variable \(X^{(1)}\) and the Moving Minimum of a Random Variable \(X^{(2)}\) at Index \(t\). It is calculated as follows.

\(\textrm{Range}_t\left(X^{(1)},X^{(2)},n\right) = \max_t\left(X^{(1)},n\right) - \min_t\left(X^{(2)},n\right)\)#### Moving Summation

This operation returns the sum of a set of values in a moving window of Length \(n\). Our notation for the Moving Sum of a Random Variable \(X\) at Index \(t\) is \(\mathrm{sum}_t(X,n)\), and it is calculated as follows.

\(\mathrm{sum}_t(X,n) = X_{t - n + 1} + X_{t - n + 2} + \cdots + X_t\)We can express this as a Summation as follows.

\(\displaystyle{\mathrm{sum}_t(X,n) = \sum_{i = t - n + 1}^t X_i}\)In the event that there are not yet \(n\) values in the moving window (that is, \(t < n - 1\)), the Moving Summation is calculated as follows.

\(\displaystyle{\mathrm{sum}_t(X,n) = X_0 + X_1 + \cdots + X_t = \sum_{i = 0}^t X_i}\)#### Multiplication

We make occasional use of Pi (\(\Pi\)) notation for multiplication.

For the list of \(n\) numbers \(X_1,X_2,...,X_n\), we denote their product as follows.

\(\displaystyle{\prod_{i = 1}^n}X_i = X_1 \cdot X_2 \cdot \cdots \cdot X_n\)

**product sign**.

**index of multiplication**, or simply the

**index**. It functions as a counter from \(1\) to \(n\).

**lower limit of multiplication**.

**upper limit of multiplication**.

**multiplicand**.

#### Rounding Function

The rounding function returns the integer that is closest to a given number. The notation for the rounding function of a number \(X\) is \([X]\).

Example: \([5.1] = 5\)

Example: \([5.8] = 6\)

#### Summation

We make frequent use of Sigma (\(\Sigma\)) notation for summation.

For the list of \(n\) numbers \(X_1,X_2,...,X_n\), we denote their sum as follows.

\(\displaystyle{\sum_{i = 1}^n}X_i = X_1 + X_2 + \cdots + X_n\)

**summation sign**.

**index of summation**, or simply the

**index**. It functions as a counter from \(1\) to \(n\).

**lower limit of summation**.

**upper limit of summation**.

**summand**.

#### Welles Summation

This operation returns the sum of a set of values in a moving window of Length \(n\). Our notation for the Moving Sum of a Random Variable \(X\) at Index \(t\) is \(WS_t(X,n)\), and it is calculated as follows.

\(WS_t(X,n) = \left\{ \begin{matrix} X_0 & t = 0 \\ WS_{t - 1}(X,n) + X_t & 0 < t < n \\ WS_{t - 1}(X,n) - WS_{t - 1}(X,n)/n + X_t & t \geq n \end{matrix}\right .\)

### Parameters

Parameters are variables whose values are either entered by the user as Inputs, calculated from Input values, automatically generated by Auto Looping, or automatically generated by internal looping.

- \(\Delta\alpha\) - Acceleration Increment - Appears in Parabolic
- \(\alpha_{max}\) - Max Acceleration Factor - Appears in Parabolic
- \(\alpha_S\) - Start Acceleration Factor - Appears in Parabolic
- \(c\) - Currency Value Per Tick - This is set through
**Chart >> Chart Settings >> Advanced Settings 2**. - \(c\) - Smoothing Constant - Appears in several moving averages, such as Moving Average - Adaptive and Moving Average - Exponential. This may be subscripted, e.g. \(c_F\), \(c_S\), etc.
- \(i\) - Variable Chart Bar Index Value - Usually varies from some past value of the Index up to the Current Index Value \(t\).
- \(k\) - Offset
- \(l\) - Line Value - Appears in Inverse Fisher Transform and Inverse Fisher Transform with RSI
- \(\mu\) - ATR Multiplier - Appears in Volatility Trend Indicator.
- \(n\) - Length - This may be subscripted, e.g. \(n_1\), \(n_{RSI}\).
- \(N^{(1)}(n)\) - Appears in Detrended Oscillator
- \(N^{(2)}(n)\) - Appears in Detrended Oscillator
- \(\phi_D\) - Divergence Threshold in Degrees - Appears in Divergence Detector
- \(\phi_O\) - Opposite Slope Divergence Threshold in Degrees - Appears in Divergence Detector
- \(s\) - Tick Size - This is set through
**Chart >> Chart Settings >> Main Settings**. - \(t\) - Current Chart Bar Index Value
- \(\tau\) - Current Chart Bar Number
- \(v\) - Multiplier (in T3) or Value (in Bands/Envelope) or Value Per Point (in Study Angle)
- \(y^{(H)}\) - High Threshold - Appears in Rate of Change Oscillator Type II
- \(y^{(L)}\) - Low Threshold - Appears in Rate of Change Oscillator Type II

### Random Variables

Random Variables are variables whose values are determined by the outcome of an experiment. For our purposes, Random Variables are almost always volumes, prices or Statistical Functions of these.

When we refer to the value of a Random Variable at Index \(t\), we use a subscript to indicate this. For instance, the value of the Random Variable **Input Data** \(X\) at Index \(t\) is denoted as \(X_t\).

- \(C\) - Closing Price - This may be superscripted, e.g. \(C^{(1)}\), \(C^{(HA)}\), \(C^{(-1)}\), etc.
- \(H\) - High Price - This may be superscripted, e.g. \(H^{(1)}\), \(H^{(HA)}\), \(H^{(-1)}\), etc.
- \(L\) - Low Price - This may be superscripted, e.g. \(L^{(1)}\), \(L^{(HA)}\), \(L^{(-1)}\), etc.
- \(n_t^{(NZ)}\) - Number of Nonzero values of \(X\) - Appears in Moving Average - Simple Skip Zeros
- \(N^{(P)}\) - Number of Prices - Appears in Numbers Bars Avg Volume Per Price Graph
- \(N\) - Number of Trades - This may be superscripted, e.g. \(N^{(ask)}\), \(N^{(bid)}\), etc.
- \(O\) - Opening Price - This may be superscripted, e.g. \(O^{(1)}\), \(O^{(HA)}\), \(O^{(-1)}\), etc.
- \(OI\) - Open Interest
- \(P\) - Price - This may be superscripted, e.g. \(P^{(ask)}\), \(P^{(bid)}\), etc.
- \(R\) - +/- Volume - Appears in Volume Zone Oscillator
- \(S\) - Study Reference - Appears in Color Bar Based On Above/Below Study and Divergence Detector
- \(V\) - Volume - This may be superscripted, e.g. \(V^{(ask)}\), \(V^{(bid)}\), etc.
- \(X\) - Input Data - These may be superscripted, e.g. \(X^{(1)}\), \(X^{(2)}\).

### Statistical Functions

Statistical Functions take on a value at each Current Index Value \(t\). Unless otherwise stated, the value of a Statistical Function is 0 prior to the starting value of \(t\). We refer to the value of a Statistical Function at Index \(t\) by using a subscript, and we write any Inputs for the Statistical Function in parentheses. For instance, the value of the Statistical Function Moving Average - Simple of **Input Data** \(X\) with **Length** \(n\) at Index \(t\) is denoted as \(MA_t(X,n)\).

When a Statistical Function is used as a Random Variable for another Statistical Function, we indicate this by omitting its subscript. For instance, the value of the Exponential Moving Average of \(X\) with **Length** \(n\) at Index \(t\) is denoted as \(EMA_t(X,n)\). If we take the Exponential Moving Average of \(EMA_t(X,n)\), again with **Length** \(n\), we denote its value at Index \(t\) as \(EMA_t(EMA(X,n),n)\). Here, \(EMA(X,n)\) is a random variable corresponding to the first Exponential Moving Average.

When we list the arguments of Statistical Functions, we list only those that have numerical values and that are input by the user. We omit all others. As an example, in the notation for the Bar Difference study, we omit the Input **Calculate Difference in Price Ticks** from the list of arguments because it is not numerical. As another example, in the notation for the Q Stick study, we omit the random variables \(C\) and \(O\) from the list of arguments because these are not input by the user.

When alphabetizing the list of Statistical Functions, we observe the following conventions.

- \(\% B_t(X,n,v)\) - Bollinger Bands: %B
- \(\% \Delta X^{(PC)}_t\) - Percent Change Since Previous Close
- \(\% \Delta X^{(O)}_t(v)\) - Percent Change Since Open
- \(\% R_t\left(X^{(High)},X^{(Low)},X^{(Last)},n\right)\) - Williams' %R
- \(a_t(X,n)\) - Intercept of Least Squares Regression Line - Appears in Moving Linear Regression / Moving Average - Linear Regression
- \(AC_t(n_L,n_S,n_{Sig})\) - Bill Williams AC
- \(ACDC_t(X,n_1,n_2,n_3,n_4)\) - AC/DC Histogram
- \(AD_t\) - Accumulation Distribution - Appears in Chaikin Oscillator
- \(ADF_t\) - Accumulation/Distribution Flow
- \(\overline{ADF}_t(n)\) - Moving Average of Accumulation/Distribution Flow
- \(AdjVal_t(X,n)\) - Adjusted Value - Appears in Cumulative Adjusted Value
- \(ADX_t(n_{DX},n_{ADX})\) - ADX - Also appears in ADXR
- \(ADXR_t(n_{DX},n_{ADX},n_{ADXR})\) - ADXR
- \(AMA_t(X,n,c_F,c_S)\) - Moving Average - Adaptive
- \(AMAHigh_t(X,n,c_F,c_S)\) - Appears in Moving Average - Adaptive Binary Wave
- \(AMALow_t(X,n,c_F,c_S)\) - Appears in Moving Average - Adaptive Binary Wave
- \(AI^{(Down)}_t\left(X^{(Low)},n\right)\) - Aroon Indicator Down
- \(AI^{(Up)}_t\left(X^{(High)},n\right)\) - Aroon Indicator Up
- \(AO_t(X,n_1,n_2)\) - Awesome Oscillator, aka Bill Williams Awesome Oscillator
- \(AO_t\left(X^{(High)},X^{(Low)},n\right)\) - Aroon Oscillator
- \(Avg^{(1)}_t(n_L)\) - First Average - Appears in Bill Williams AC
- \(Avg^{(2)}_t(n_S)\) - Second Average - Appears in Bill Williams AC
- \(Avg^{(3)}_t(n_L,n_S)\) - Third Average - Appears in Bill Williams AC
- \(Avg^{(4)}_t(n_L,n_S,n_{Sig})\) - Fourth Average - Appears in Bill Williams AC
- \(B_t(n,v)\) - Buy Price - Appears in Greatest Swing Value
- \(b_t(X,n)\) - Slope of Least Squares Regression Line - Appears in Moving Linear Regression / Moving Average - Linear Regression
- \(B^{(+)}_t(n,v)\) - Appears in Murrey Math
- \(B^{(-)}_t(n,v)\) - Appears in Murrey Math
- \(BarDiff_t\left(X^{(1)},X^{(2)},k\right)\) or \(BarDiff_t\left(X^{(1)},X^{(2)},k,s\right)\) - Bar Difference
- \(BB^{(B)}_t(X,n,v)\) - Bottom Band - Appears in Bollinger Bands and related studies
- \(BB^{(D)}_t(n)\) - Bottom Band - Appears in Donchian Channel
- \(BB^{(E)}_t(X,v)\) or \(BB^{(E)}_t(X,v,s)\) - Bottom Band - Appears in Bands/Envelope
- \(BB^{(K)}_t(X,n_K,n_{TR},v_B)\) - Bottom Band - Appears in Keltner Channel
- \(BB^{(MAE)}_t(X,n)\) - Bottom Band - Appears in Moving Average Envelope
- \(BB^{(\sigma)}_t(X,n,v)\) - Bottom Band - Appears in Standard Deviation Bands
- \(BB^{(SE)}_t(X,n)\) - Bottom Band - Appears in Standard Error Bands
- \(BB^{(Starc)}_t(X,n_S,n_{TR},v_B)\) - Bottom Band - Appears in Starc Bands
- \(BearPow_t(n)\) - Bear Power - Appears in Elder Ray
- \({BEB}^{(H)}_t(X,n,v_E)\) - Bottom Extreme Band - Appears in Hurst Bands
- \({BIB}^{(H)}_t(X,n,v_I)\) - Bottom Inner Band - Appears in Hurst Bands
- \({BOB}^{(H)}_t(X,n,v_O)\) - Bottom Outer Band - Appears in Hurst Bands
- \(BOP_t\) - Balance of Power
- \(\overline{BOP}_t(n)\) - Average Balance of Power
- \(Bot^{(i)}_t(n,v_i)\) - Bottom \(i\), \((i = 1,2)\) - Appears in Moving Average - Block
- \(BP_t(n_{BS})\) - Buy Power - Appears in Demand Index
- \(\overline{BP}_t\left(n_{BS},n_{\overline{BS}}\right)\) - Average Buy Power - Appears in Demand Index
- \(BR_t(X,n_B,v_B,n_K,n_{\overline{TR}},v_K)\) - Bands Ratio - Appears in Bollinger Squeeze
- \(BS_t\) - Buy Swing - Appears in Greatest Swing Value
- \(\overline{BS}_t(n)\) - Average Buy Swing - Appears in Greatest Swing Value
- \(BullPow_t(n)\) - Bull Power - Appears in Elder Ray
- \(BW_t(X,n,c_F,c_S,f)\) - Binary Wave - Appears in Moving Average - Adaptive Binary Wave
- \(BW_t(X,n,v)\) - Bollinger Bands: Bandwidth
- \(c_t(X,n)\) - Smoothing Constant - Appears in Moving Average - Adaptive
- \(CBI^{(1)}_t\left(X, n_{RSI}^{(1)}, n_M, n_{RSI}^{(2)}, n_{MA}^{(1)}\right)\) - First Index of the Connie Brown Composite Index
- \(CBI^{(2)}_t\left(X, n_{RSI}^{(1)}, n_M, n_{RSI}^{(2)}, n_{MA}^{(1)}, n_{MA}^{(2)}\right)\) - Second Index of the Connie Brown Composite Index
- \(CBI^{(3)}_t\left(X, n_{RSI}^{(1)}, n_M, n_{RSI}^{(2)}, n_{MA}^{(1)}, n_{MA}^{(3)}\right)\) - Third Index of the Connie Brown Composite Index
- \(CC_t(X,n)\) - Coppock Curve
- \(CCI_t(X,n,v)\) - Commodity Channel Index
- \(CFO_t(X,n)\) - Chande Forecast Oscillator
- \(CLV_t\) - Close Level Value - Appears in Chaikin Money Flow
- \(CMF_t(n)\) - Chaikin Money Flow
- \(CMO_t(X,n_{CMO})\) - Chande Momentum Oscillator
- \(CO_t(n_L,n_S,v)\) - Chaikin Oscillator
- \(CS_{i - n}(X,n)\) - Chikou Span
- \(CSF_t(X,n)\) - Custom Smoothing Function - Appears in Price Momentum Oscillator
- \(CumAdjVal_t(X,n)\) - Cumulative Adjusted Value
- \(CVol_t(n)\) - Volatility - Chaikins
- \(D_t(X)\) - Downward Change in \(X\) - Appears in RSI - Also appears in Chande Momentum Oscillator, though defined slightly differently there
- \(D_t(X,n)\) - Downward Change in \(X\) over \(n\) Bars - Appears in Relative Momentum Index
- \(\Delta (\Delta C_t)\) - Bar Price Change Difference - 2 Chart
- \(\Delta MA_t(X,n_1,n_2)\) - Moving Average Difference - Also appears in AC/DC Histogram
- \(\Delta MACD_t(X,n_F,n_S,n_M)\) - MACD Difference - Appears in MACD
- \(\Delta MACD^{(3/10)}_t(X,n_F,n_S,n_{3/10})\) - 3/10 Oscillator Difference - Appears in 3/10 Oscillator
- \(\Delta VWMACD_t(X,n_F,n_S,n_M)\) - Volume Weighted MACD Difference - Appears in MACD - Volume Weighted
- \(\Delta X_t(n)\) - Rate of Change - Points
- \(DeM_t(n)\) - Demarker
- \(DeM_t^{(I)}\left(X^{(H)},X^{(L)},n_{DeM}^{(1)},n_{DeM}^{(2)}\right)\) - Demarker Oscillator Type I
- \(DeM_t^{(II)}\left(X^{(H)},X^{(L)},X^{(C)},n_{DeM}^{(1)},n_{DeM}^{(2)}\right)\)
- \(DeM_t^{(\max)}\) - Max Demarker
- \(DeM_t^{(\min)}\) - Min Demarker
- \(DeMax_t^{(I)}\left(X^{(H)},n_{DeM}^{(1)}\right)\) - Max DeMarker Type I - Appears in Demarker Oscillator Type I
- \(DeMax_t^{(II)}\left(X^{(H)},X^{(L)},X^{(C)},n_{DeM}^{(1)}\right)\) - Max DeMarker Type II - Appears in Demarker Oscillator Type II
- \(DeMin_t^{(I)}\left(X^{(L)},n_{DeM}^{(1)}\right)\) - Min DeMarker Type I - Appears in Demarker Oscillator Type I
- \(DeMin_t^{(II)}\left(X^{(H)},X^{(L)},X^{(C)},n_{DeM}^{(1)}\right)\) - Min DeMarker Type II - Appears in Demarker Oscillator Type II
- \(DEMA_t(X,n)\) - Moving Average - Double Exponential
- \(DI_t\left(n_{BS}, n_{\overline{BS}}\right)\) - Demand Index
- \(\overline{DI}_t\left(n_{BS}, n_{\overline{BS}}, n_{\overline{DI}}\right)\) - Average Demand Index
- \(DI_t^{(+)}(n_{DX})\) - Positive Directional Indicator - Appears in Directional Movement Index - Also appears in ADX, though it is calculated differently there
- \(DI_t^{(-)}(n_{DX})\) - Negative Directional Indicator - Appears in Directional Movement Index - Also appears in ADX, though it is calculated differently there
- \(Dir_t(X,n)\) - Direction - Appears in Moving Average - Adaptive
- \(Dir_t(X,n,\mu,DPL_{\max})\) - Direction - Appears in Volatility Trend Indicator - Differs from the function that appears in Moving Average - Adaptive
- \(Dir^{(i)}_t(n,v_i)\) - Direction \(i\), \((i = 1,2)\) - Appears in Moving Average - Block
- \(DM_t^{(+)}\) - Positive Directional Movement - Appears in Directional Movement Index and ADX
- \(DM_t^{(-)}\) - Negative Directional Movement - Appears in Directional Movement Index and ADX
- \(DMO_t(n_{DX})\) - Directional Movement Oscillator
- \(DO_t(n)\) - Detrended Oscillator
- \(DO^{(DN)}_t(X,n)\) - Detrended Oscillator - DiNapoli
- \(DPL_t(X,n,\mu,DPL_{\max})\) - Dynamic Period Length - Appears in Volatility Trend Indicator
- \(DR_t\) - Daily Range - Appears in Average Daily Range
- \(\overline{DR}_t(n)\) - Average Daily Range
- \(DS_t(n,n_{MA})\) - Double Stochastic
- \(DS^{(B)}_t(n_{HL},n_{MA},n_S)\) - Double Stochastic - Bressert
- \(DT^{(SD)}_t(n_{RSI},n_{S},n_{SK},n_{SD})\) - Moving Average of \(D^{(SK)}_t(n_{RSI},n_{S},n_{SK})\) - Appears in DT Oscillator
- \(DT^{(SK)}_t(n_{RSI},n_{S},n_{SK})\) - Moving Average of \(100\) times Stochastic RSI - Appears in DT Oscillator
- \(DX_t(n_{DX})\) - Directional Movement Index - Appears in ADX and ADXR
- \(E_t\left[\left(X - SMA(X,n)\right)\right]^2\) - Second Central Moment - Appears in Kurtosis
- \(E_t\left[\left(X - SMA(X,n)\right)\right]^4\) - Fourth Central Moment - Appears in Kurtosis
- \(EMA_t(X,n)\) - Moving Average - Exponential
- \(EMA_t^{(j)}(X,n)\) - \(j-\)fold composition of the Exponential Moving Average with itself - Appears in Moving Average - Double Exponential, Moving Average - Triple Exponential, T3, and TRIX
- \(EMV_t(k)\) - Arms Ease of Movement
- \(\overline{EMV}_t(k,n)\) - Moving Average of Arms Ease of Movement
- \(EP_t\left(X^{(High)}, X^{(Low)}\right)\) - Extreme Point - Appears in Parabolic
- \(Fast\% D_t(X^{(High)},X^{(Low)},X^{(Close)},n_{FastK},n_{FastD})\) - Fast %D (aka Slow %K) - Appears in KD - Fast and KD - Slow
- \(Fast\% D_t^{(1)}(n,n_{MA})\) - First Fast %D - Appears in Double Stochastic and Double Stochastic - Bressert
- \(Fast\% D_t^{(2)}(n,n_{MA})\) - Second Fast %D - Appears in Double Stochastic and Double Stochastic - Bressert
- \(Fast\% K_t(X^{(High)},X^{(Low)},X^{(Close)},n_{FastK})\) - Fast %K - Appears in KD - Fast
- \(Fast\% K_t^{(1)}(n)\) - First Fast %K - Appears in Double Stochastic and Double Stochastic - Bressert
- \(Fast\% K_t^{(2)}(n,n_{MA})\) - Second Fast %K - Appears in Double Stochastic and Double Stochastic - Bressert
- \(FCV_t(X,s,c)\) - Full Contract Value
- \(FI_t\) - Force Index
- \(\overline{FI}_t(n)\) - Force Index Average
- \(FT_t(X,n)\) - Fisher Transform
- \(GHLA_t(n)\) - Gann Hi Lo Activator
- \({HH}_t\) - Highest High - Appears in Clear Method Swing Line
- \({HH}_t^{(i)}\) - Highest High for Case \(i\), \((i = 1, 2, 3)\) - Appears in Clear Method Swing Line
- \(HiLo_t(n)\) - High Low Function - Appears in Gann Hi Lo Activator
- \({HL}_t\) - Highest Low - Appears in Clear Method Swing Line
- \({HL}_t^{(i)}\) - Highest Low for Case \(i\), \((i = 1, 2, 3)\) - Appears in Clear Method Swing Line
- \(HLDiff_t(n)\) - Difference between Highest High and Lowest Low - Appears in HL Volatility
- \(HLVol_t(n)\) - HL Volatility
- \(HMA_t(X,n)\) - Moving Average - Hull
- \(HPI_t(v_1,v_2,v_3)\) - Herrick Payoff Index
- \(HPI^*_t(v_1,v_2)\) - Intermediate function for calculating Herrick Payoff Index
- \(HVol_t(X,n,N)\) - Volatility - Historical
- \(HVR_t(n_S,n_L)\) - Historical Volatility Ratio
- \(I_t(n,v)\) - Appears in Murrey Math
- \(IB_t\) - Inside Bar
- \(IEB_t\) - Inside or Equals Bar
- \(IFT_t(X)\) - Inverse Fisher Transform
- \(\overline{IFT}_t(X,n)\) - Moving Average of the Inverse Fisher Transform
- \(Inertia^{(1)}_t(n_{RVI},n_{LR})\) - Inertia
- \(Inertia^{(2)}_t(n_\sigma,n_{RVI},n_{LR})\) - Inertia 2
- \(J_t(X^{(High)},X^{(Low)},X^{(Close)},n_{FastK},n_{FastD},n_{SlowD})\) - J Line - Appears in KDJ
- \(Jaw_t(X,n_J)\) - Jaw of Bill Williams Alligator
- \(K_t(X,n)\) - Kurtosis
- \(KS_t\left(X^{(High)},X^{(Low)},n_{KS}\right)\) - Kijun-Sen
- \(L(n)\) - Lag - Appears in Moving Average - Zero Lag Exponential
- \(Label_t\) - Label - Appears in Market Structure MSL/MSH
- \({LH}_t\) - Lowest High - Appears in Clear Method Swing Line
- \({LH}_t^{(i)}\) - Lowest High for Case \(i\), \((i = 1, 2, 3)\) - Appears in Clear Method Swing Line
- \(Lips_t(X,n_L)\) - Lips of Bill Williams Alligator
- \({LL}_t\) - Lowest Low - Appears in Clear Method Swing Line
- \({LL}_t^{(i)}\) - Lowest Low for Case \(i\), \((i = 1, 2, 3)\) - Appears in Clear Method Swing Line
- \(LR_t(X)\) - Logarithmic Return - Appears in Volatility - Historical and Historical Volatility Ratio
- \(LRI_t(X,n)\) - Linear Regression Indicator - Appears in Moving Linear Regression / Moving Average - Linear Regression
- \(LRMA_t(X,n)\) - Moving Average - Linear Regression
- \(LRS_t(X,n)\) - Linear Regressive Slope
- \(M_t(n,v)\) - Appears in Murrey Math
- \(M_t(X,n)\) - Momentum
- \(\overline{M}_t(X,n,n_{MA})\) - Moving Average of Momentum
- \(MA_t(X,n)\) - Moving Average - Simple
- \(MACD_t(X,n_F,n_S)\) - MACD
- \(MACD^{(3/10)}_t(X,n_F,n_S)\) - 3/10 Oscillator
- \(\overline{MACD}_t(X,n_F,n_S,n_M)\) - MACD Moving Average - Appears in MACD
- \(\overline{{MACD}}^{(3/10)}_t(X,n_F,n_S,n_{3/10})\) - 3/10 Oscillator Moving Average - Appears in 3/10 Oscillator
- \(MACDL_t(X,n_F,n_S)\) - MACD Leader
- \(\max_t(X,n)\) - Moving Maximum - Appears in several studies, such as Highest High/Lowest Low Over N Bars and Donchian Channel
- \(MaxRSI_t(X,n,n_{HL})\) - Maximum RSI - Appears in Stochastic RSI
- \(MB^{(D)}_t(n)\) - Middle Band - Appears in Donchian Channel
- \(MEMA^{(1)}_t(X,n)\) - McClellan Exponential Moving Average Type 1 - Appears in McClellan Oscillator - 1 Chart
- \(MEMA^{(2)}_t(X,n)\) - McClellan Exponential Moving Average Type 2 - Appears in McClellan Summation Index - 1 Chart
- \(MF^{(+)}_t\) - Positive Money Flow - Appears in Money Flow Index
- \(MF^{(-)}_t\) - Negative Money Flow - Appears in Money Flow Index
- \(MFI_t(k)\) - Market Facilitation Index
- \(MFI_t(n)\) - Money Flow Index
- \(MFR_t(n)\) - Money Flow Ratio - Appears in Money Flow Index
- \(Mid^{(i)}_t(n,v_i)\) - Middle \(i\), \((i = 1,2)\) - Appears in Moving Average - Block
- \(\min_t(X,n)\) - Moving Minimum - Appears in several studies, such as Highest High/Lowest Low Over N Bars and Donchian Channel
- \(MinRSI_t(X,n,n_{HL})\) - Minimum RSI - Appears in Stochastic RSI
- \(MLR_t(X,n)\) - Moving Linear Regression
- \(MMed_t(X,n)\) - Moving Median
- \(MML_t(n,v,\ell)\) - Murrey Math Lines
- \(MO_t\) - McClellan Oscillator - 1 Chart
- \(MSH_t\) - Market Structure High - Appears in Market Structure MSL/MSH
- \(MSI_t\) - McClellan Summation Index - 1 Chart
- \(MSL_t\) - Market Structure Low - Appears in Market Structure MSL/MSH
- \(ND_t\) - Negative Divergence - Appears in Divergence Detector
- \(NR_t(n)\) - Narrow Range for
**NR n**lookback scheme - Appears in Narrow Range Bar - \(NR_t(n,x)\) - Narrow Range for
**x Bar NR**lookback scheme - Appears in Narrow Range Bar - \(NRLB_t(n,x)\) - Narrow Range of Leading Bar for
**x Bar NR**lookback scheme - Appears in Narrow Range Bar - \(NVI_t(X,NVI_0)\) - Negative Volume Index
- \(OB_t\) - Outside Bar
- \(OC_t(n,v)\) - Octave Count - Appears in Murrey Math
- \(OI^*_t\) - Modified Open Interest - Appears in Herrick Payoff Index
- \(OI^{(\pm)}_t(n)\) - Signed Open Interest - Appears in On Balance Open Interest - Short Term
- \(OI^{(OB)}_t\) - On Balance Open Interest
- \(OI^{(OB)}_t(n)\) - On Balance Open Interest - Short Term
- \(P_t(X,n_{PS})\) - Smoothed or Unsmoothed Price - Appears in Adaptive RSI Moving Average with Smoothing
- \(\overline{P}_t\) - Average Price - Appears in Average Price For Bar - Also appears in Relative Vigor Index 2 with superscripts: \(\overline{P}^{(C-O)}_t\) and \(\overline{P}^{(H-L)}_t\)
- \(PD_t\) - Positive Divergence - Appears in Divergence Detector
- \(PFE_t(X,n)\) - Polarized Fractal Efficiency
- \(PFE^{(S)}_t(X,n)\) - Smoothed Polarized Fractal Efficiency
- \(\pi^{(i)}_t(X,n,\mu,DPL_{\max})\), \(i = 1,2,3\) - Period 1, 2, and 3 - Appear in Volatility Trend Indicator
- \(PMO_t(X,n_1,n_2)\) - Price Momentum Oscillator Line
- \(\overline{PMO}_t(X,n_1,n_2,n_{Sig})\) - Price Momentum Oscillator Signal Line
- \(POVI_t\) - Price, Open Interest, Volume
- \(PPO_t(X,n_L,n_S)\) - Percentage Price Oscillator
- \(PrevBar_t(X)\) - Previous Bar Close
- \(PVI_t(X,PVI_0)\) - Positive Volume Index
- \(PVT_t\) - Price Volume Trend
- \(Q_t\left(n_{BS}, n_{\overline{BS}}\right)\) - Quotient - Appears in Demand Index
- \(QStick_t(n)\) - Q Stick
- \(R_t(X,n)\) - Rank - Appears in Stochastic - Percentile
- \(R_t(X,n,n_{MA},n_{\sigma})\) - Ratio - Appears in Bollinger Squeeze 3
- \(R_t(X,n_{PS},n_{ARSI},n_{RSIS})\) - Smoothed or Unsmoothed RSI - Appears in Adaptive RSI Moving Average with Smoothing
- \(\textrm{Range}^{(MMI)}_t(n,v)\) - Murrey Math Interval Range - Appears in Murrey Math
- \(\overline{\textrm{Range}}_t\left(X^{(1)},X^{(2)},n,n_{Avg}\right)\) - Average Range - Appears in Demand Index
- \(\textrm{Range}^{(Rel)}_t\left(X^{(1)},X^{(2)},X^{(3)},n\right)\) - Relative Range - Appears in Stochastic Momentum Indicator
- \(RF_t\) - Rotation Factor
- \(RF^{(i)}_t\), \(i = 1,2,3,raw\) - Various stages of the calculation of the Rotation Factor
- \(RMF_t\) - Raw Money Flow - Appears in Money Flow Index
- \(RCB_t\) - Range of Current Bar - Appears in Narrow Range Bar and Wide Range Bar
- \(RCG_t(x)\) - Range of Current Group - Appears in Narrow Range Bar and Wide Range Bar
- \(REI_t\left(X^{(HC)}, X^{(LC)}, n, n_L^{(1)}, n_L^{(2)}, n_L^{(3)}\right)\) - Range Expansion Index
- \(Repulse_t(n)\) - Repulse
- \(\rho_t(X,Y,n)\) - Correlation Coefficient
- \(RMI_t(X,n,n_{MA})\) - Relative Momentum Index
- \(RMO_t(X,n_1,n_2,n_4)\) - Rahul Mohindar Oscillator
- \(ROC_t(X,n,v)\) - Rate of Change - Percentage
- \(ROC_t^{(I)}\left(X,n_{ROC}\right)\) - Rate of Change Oscillator Type I
- \(ROC_t^{(II)}\left(X,X^{(H)},X^{(L)},n_{ROC},y^{(H)},y^{(L)}\right)\) - Rate of Change Oscillator Type II
- \(\overline{ROC}_t(X,n,v,n_1)\) - Average Rate of Change - Percentage - Appears in Price Momentum Oscillator
- \(RSI_t(X,n_{RSI})\) - RSI
- \(\overline{RSI}_t(X,n_{RSI},n)\) - Moving Average of RSI
- \(\overline{RSI}_t(X,n_{PS},n_{ARSI},n_{RSIS},v)\) - Adaptive RSI Moving Average with Smoothing
- \(RSI^*(X,n_{RSI})\) - Transformation of RSI - Appears in Inverse Fisher Transform with RSI
- \(\overline{RSI^*}(X,n_{RSI},n_{\overline{RSI}})\) - Moving Average of Transformation of RSI - Appears in Inverse Fisher Transform with RSI
- \(RV_t\) - Range Volume - Appears in Accumulation/Distribution
- \(RVI_t\) - Relative Vigor Index - Appears in Relative Vigor Index 1 and Relative Vigor Index 2
- \(\overline{RVI}^{(1)}_t(n)\) - Smoothed Relative Vigor Index 1 - Appears in Relative Vigor Index 1
- \(\overline{RVI}^{(2)}_t(n)\) - Smoothed Relative Vigor Index 2 - Appears in Relative Vigor Index 2
- \(RVIX_t(n_\sigma,n_{RVIX})\) - Relative Volatility Index - Appears in Inertia 2
- \(RVIX^{(D)}_t(n_\sigma)\) - Relative Volatility Index Down - Appears in Inertia 2
- \(\overline{RVIX}^{(D)}_t(n_\sigma,n_{RVIX})\) - Smoothed Relative Volatility Index Down - Appears in Inertia 2
- \(RVIX^{(U)}_t(n_\sigma)\) - Relative Volatility Index Up - Appears in Inertia 2
- \(\overline{RVIX}^{(U)}_t(n_\sigma,n_{RVIX})\) - Smoothed Relative Volatility Index Up - Appears in Inertia 2
- \(RWI^{(High)}_t(n)\) - High Random Walk Indicator
- \(RWI^{(Low)}_t(n)\) - Low Random Walk Indicator
- \(S_t(n,v)\) - Sell Price - Appears in Greatest Swing Value
- \(SAR_t\left(X^{(High)}, X^{(Low)}, \alpha_S, \Delta\alpha, \alpha_{max}\right)\) - Parabolic Stop and Reverse - Appears in Parabolic
- \(SF_t(X,n_{PS},n_{ARSI},n_{RSIS},v)\) - Scaling Factor - Appears in Adaptive RSI Moving Average with Smoothing
- \(Si_t(n,v)\) - Appears in Murrey Math
- \(SI_t(X,n_B,v_B,n_K,n_{\overline{TR}},v_K)\) - Squeeze Indicator - Appears in Bollinger Squeeze 2
- \(Sig^{(1)}_t(n)\) - Signal Line - Appears in Relative Vigor Index 1
- \(Sig^{(2)}_t(n)\) - Signal Line - Appears in Relative Vigor Index 2
- \(\sigma_t(X,n)\) - Standard Deviation
- \({SL}_t\) - Clear Method Swing Line
- \(Slow\% D_t(X^{(High)},X^{(Low)},X^{(Close)},n_{FastK},n_{FastD},n_{SlowD})\) - Slow %D - Appears in KD - Slow
- \(SMA_t(X,n)\) - Moving Average - Simple
- \(SMI_t(n_K,n_D)\) - Stochastic Momentum Indicator
- \(\overline{SMI}_t(n_K,n_D,n_{EMA})\) - Average of Stochastic Momentum Indicator
- \(SMMA_t(X,n,k)\) - Smoothed Moving Average
- \(SP_t(n_{BS})\) - Sell Power - Appears in Demand Index
- \(SP_t(X,n)\) - Stochastic - Percentile
- \(\overline{SP}_t\left(n_{BS},n_{\overline{BS}}\right)\) - Average Sell Power - Appears in Demand Index
- \(\overline{SP}_t(X,n,n_{MA})\) - Moving Average of Stochastic - Percentile
- \(SR_t(n,v)\) - Appears in Murrey Math
- \(SS_t\) - Sell Swing - Appears in Greatest Swing Value
- \(\overline{SS}_t(n)\) - Average Sell Swing - Appears in Greatest Swing Value
- \(SSA_t(n_{TS},n_{KS})\) - Senkou Span A
- \(SSB_t\left(X^{(High),}, X^{(Low)}, n\right)\) - Senkou Span B
- \(ST^{(1)}_t(X,n_1,n_2)\) - Swing Trade 1 - Appears in Rahul Mohindar Oscillator
- \(ST^{(2)}_t(X,n_1,n_2,n_3)\) - Swing Trade 2 - Appears in Rahul Mohindar Oscillator
- \(ST^{(3)}_t(X,n_1,n_2,n_3)\) - Swing Trade 3 - Appears in Rahul Mohindar Oscillator
- \(StochRSI_t(n,n_{HL})\) - Stochastic RSI
- \(sum_t(X)\) - Summation
- \(Sum^{(1)}_t(n_L)\) - First Sum - Appears in Bill Williams AC
- \(Sum^{(2)}_t(n_S)\) - Second Sum - Appears in Bill Williams AC
- \(Sum^{(4)}_t(n_L,n_S,n_{Sig})\) - Fourth Sum - Appears in Bill Williams AC
- \(SWWMA_t(X,n)\) - Moving Average - Sine Wave Weighted
- \(SynthVIX_t(n)\) - Synthetic VIX
- \(SZMA_t(X,n)\) - Moving Average - Simple Skip Zeros
- \(T_t^{(Down)}\left(X^{(Low)},n\right)\) - Index of most recent low of \(X^{(Low)}\) - Appears in Aroon Indicator
- \(T_t^{(Up)}\left(X^{(High)},n\right)\) - Index of most recent high of \(X^{(High)}\) - Appears in Aroon Indicator
- \(T3_t(X,n,v)\) - T3
- \(TB^{(B)}_t(X,n,v)\) - Top Band - Appears in Bollinger Bands and related studies
- \(TB^{(D)}_t(n)\) - Top Band - Appears in Donchian Channel
- \(TB^{(E)}_t(X,v)\) or \(BB^{(E)}_t(X,v,s)\) - Top Band - Appears in Bands/Envelope
- \(TB^{(K)}_t(X,n_K,n_{TR},v_B)\) - Top Band - Appears in Keltner Channel
- \(TB^{(MAE)}_t(X,n)\) - Top Band - Appears in Moving Average Envelope
- \(TB^{(\sigma)}_t(X,n,v)\) - Top Band - Appears in Standard Deviation Bands
- \(TB^{(SE)}_t(X,n)\) - Top Band - Appears in Standard Error Bands
- \(TB^{(Starc)}_t(X,n_S,n_{TR},v_B)\) - Top Band - Appears in Starc Bands
- \({TEB}^{(H)}_t(X,n,v_E)\) - Top Extreme Band - Appears in Hurst Bands
- \(Teeth_t(X,n_T)\) - Teeth of Bill Williams Alligator
- \(TEMA_t(X,n_1,n_2)\) - Moving Average - Triple Exponential
- \(TH_t\) - True High - Appears in Ultimate Oscillator and Price, Open Interest, Volume
- \(\theta_t(X,n,v)\) - Study Angle
- \({TIB}^{(H)}_t(X,n,v_I)\) - Top Inner Band - Appears in Hurst Bands
- \(TL_t\) - True Low - Appears in Ultimate Oscillator and Price, Open Interest, Volume
- \(TMA_t(X,n)\) - Moving Average - Triangular
- \({TOB}^{(H)}_t(X,n,v_O)\) - Top Outer Band - Appears in Hurst Bands
- \(Top^{(i)}_t(n,v_i)\) - Top \(i\), \((i = 1,2)\) - Appears in Moving Average - Block
- \(TR_t\) - True Range
- \(\overline{TR}_t(n)\) - Average True Range
- \(TRIX_t(X,n)\) - TRIX
- \(TS_t\left(X^{(High)},X^{(Low)},n_{TS}\right)\) - Tenkan-Sen
- \(TSI_t(X,n_L,n_S,v)\) - True Strength Index aka Ergodic
- \(TSIOsc_t(X,n_L,n_S,n_{Sig},v)\) - Oscillator Line for True Strength Index aka Ergodic
- \(TSISig_t(X,n_L,n_S,n_{Sig},v)\) - Signal Line for True Strength Index aka Ergodic
- \(TV_t(n)\) - Total Volume - Appears in Volume Zone Oscillator
- \(U_t(X)\) - Upward Change in \(X\) - Appears in RSI - Also appears in Chande Momentum Oscillator, though defined slightly differently there
- \(U_t(X,n)\) - Upward Change in \(X\) over \(n\) Bars - Appears in Relative Momentum Index
- \(UO_t(n_1,n_2,n_3)\) - Ultimate Oscillator
- \({US}_t\) - Up Swing - Appears in Clear Method Swing Line
- \({US}_t^{(i)}\) - Up Swing for Case \(i\), \((i = 1, 2, 3)\) - Appears in Clear Method Swing Line
- \(\overline{V}_t(n_{BS})\) - Average Volume - Appears in Demand Index
- \(V^{(\pm)}_t(n)\) - Signed Volume - Appears in On Balance Volume - Short Term
- \(V_t^{(N)}(n)\) - Normalized Volume
- \(V^{(OB)}_t\) - On Balance Volume
- \(V^{(OB)}_t(n)\) - On Balance Volume - Short Term
- \(Var_t(X,n)\) - Variance - Appears in Standard Deviation and Dispersion
- \(Vol_t(X,n)\) - Volatility - Appears in Moving Average - Adaptive
- \(VP_t(n)\) - Volume Position - Appears in Volume Zone Oscillator
- \(\overline{VPP}_t\) - Average Volume Per Price - Appears in Numbers Bars Avg Volume Per Price Graph
- \(VR_t\) - Volume Ratio - Appears in Bid Ask Volume Ratio
- \(\overline{VR}_t(n)\) - Average Volume Ratio - Appears in Bid Ask Volume Ratio
- \(VTI_t(X,n,\mu,DPL_{\max})\) - Volatility Trend Indicator
- \(VWMA_t(X,n)\) - Moving Average - Weighted
- \(VWMACD_t(X,n_F,n_S)\) - MACD - Volume Weighted
- \(\overline{VWMACD}_t(X,n_F,n_S,n_M)\) - Volume Weighted MACD Moving Average - Appears in MACD - Volume Weighted
- \(VZO_t(n)\) - Volume Zone Oscillator
- \(W^{(Bear)}_t(n)\) - Bearish Weighting - Appears in Repulse
- \(W^{(Bull)}_t(n)\) - Bullish Weighting - Appears in Repulse
- \(WAO_t(X,n_F,n_S)\) - Weighted Average Oscillator
- \(WAD_t\) - Accumulation Distribution - Williams
- \(WBH^{(i)}_t(n)\) - Work Box Half \(i\), \((i = 1,2)\) - Appears in Moving Average - Block
- \(WR_t(n)\) - Wide Range for
**NR n**lookback scheme - Appears in Wide Range Bar - \(WR_t(n,x)\) - Wide Range for
**x Bar NR**lookback scheme - Appears in Wide Range Bar - \(WRLB_t(n,x)\) - Wide Range of Leading Bar for
**x Bar NR**lookback scheme - Appears in Wide Range Bar - \(WWMA_t(X,n)\) - Moving Average - Welles Wilders
- \(\Xi_t(X,n)\) - De-Lagged Price Data - Appears in Moving Average - Zero Lag Exponential
- \(\xi_t(X,n)\) - First Transformation of Price Data - Appears in Fisher Transform and Inverse Fisher Transform, though defined differently in the two studies
- \(\overline{\xi}_t(X,n)\) - Moving Average of \(\xi_t(X,n)\) - Appears in Inverse Fisher Transform
- \(\xi^*_t(X,n)\) - Second Transformation of Price Data - Appears in Fisher Transform
- \(Z_t(X,n_{\mu},n_{\sigma})\) - Z-Score
- \(ZLEMA_t(X,n)\) - Moving Average - Zero Lag Exponential

*Last modified Tuesday, 05th November, 2019.