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Calculate product of modified bessel functions of first kind & exponential?

GROUPS:

There is a equation which goes like:

$$\sum_{n=-\infty}^{\infty}I_n(x)e^{-x}=1$$

where $I_n(x)$ is the Modifed bessel function of first order and $e^{-x}$ is the exponential function.This is a well know relation, which hold good for any value of x. But, when I tried to do this in Mathematica, it's not giving any answer. My code goes like this:

Sum[BesselI[n, x]*E^(-x), {n, -Infinity, Infinity}]

Any help will be really appreciated.

Thanks in advance...

POSTED BY: Sreeraj T
Answer
4 months ago

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