(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

What is easiest way to summate

[tex]\sum^{\infty}_{n=1}J_n(x)[i^n+(-1)^ni^{-n}][/tex]

where ##i## is imaginary unit.

2. Relevant equations

3. The attempt at a solution

I don't need to write explicit Bessel function so in sum could stay

[tex]C_1J_(x)+C_2J_2(x)+...[/tex]

Well I see that terms in the sum will be

[tex]2iJ_1(x)-2J_2(x)+...[/tex]

But I search for more sofisticated solution. Is there any way to sum this using ##i^1=i##,##i^2=-1##,##i^3=-i##,##i^4=1##?

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Bessel function summation

**Physics Forums | Science Articles, Homework Help, Discussion**