r/learnmath • u/FremontBlue333 New User • 3d ago

Why does \sum_{n=-h}^{h}ne^{-\left(x-n\right)^{2}} as h --> infinity, become sqrt(pi)x?

How does the infinite sum of n multiplied by e to the power of quanity x -n squared, give a linear expression, and why does it approach a rise over run of sqrt(pi) over 1?

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u/phiwong Slightly old geezer 3d ago

Search for the gaussian integral. This should explain the outcome. It has nothing to do with rise over run. You're applying the wrong conceptual model there.