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# Technical Studies Reference

### Summation of Study Subgraph - Periodic

This study calculates and displays a periodic Summation of the data specified by the Study and Subgraph to Reference Input.

Let $$X$$ be a random variable denoting the data from the Study and Subgraph to Reference, and let $$X_i$$ be the value of the of this data at Index $$i$$. Let the Length Input be denoted as $$n$$. Then we denote the Summation - Periodic at Index $$t$$ for the given Input as $$\mathrm{sum}_t(X,n)$$, and we compute it for $$t \geq n - 1$$ as follows.

$$\displaystyle{\mathrm{sum}_t(X,n) = \sum_{i = t - n + 1}^tX_i}$$

For an explanation of the Sigma ($$\Sigma$$) notation for summation, refer to our description here.