bessel function plz explain 1. The problem statement, all variables and given/known data summation limits (n=j to infinity) (-a/4)**n/n!(2n_ n+j) =(-1)**j e**(-a/2) I(a/2) where j>=1 the rest are constants and I is summation index i was just solving a SHM problem involving fourier transform in which this happens to be one of the steps involving the solution. i got this solution from mathematica it seems it's a modified bessel function of 1st kind.can any one plz explain this.i know nothing about bessel function and my basics in mathematics is bit shaky. 2. Relevant equations iv(x)=summation limits 0 to infinity.(1/s!(s+1)!)*(x/2)^(2s+v) 3. The attempt at a solution i read book by arfken and others but still can't understand.now it's more confusing.i got so confused with this step i can no longer remember the actual problem.