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matematikuvol
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Homework Statement
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.
Homework Equations
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##?