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…