Bessel J function problem

Asked May 16 '14 at 22:40

Active May 16 '14 at 23:10

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Let $\xi_{0k}$ be the k-th positive zero of $J_{0}$ Bessel function. Determine the coefficients $c_k$, so that

$1 = \sum^{\infty}_{k=1} c_kJ_0(\frac{x \xi_{0k}}{2})$.

I don't see what to do, is this solvable?

edited May 16 '14 at 23:10

Antonio Vargas

asked May 16 '14 at 22:40

James

1

Here you're summing up an infinite amount of things and putting an equal sign next to it. This suggests some sort of convergence. What kind of convergence are you looking for? Almost everywhere? Pointwise? Uniform? – Cameron Williams May 16 '14 at 22:46
2

Have you seen this? http://dlmf.nist.gov/10.22#E37 Formula 10.22.37 – Antonio Vargas May 16 '14 at 23:09
its in the bible of Bessel functions, namely, Watson's book https://archive.org/details/ATreatiseOnTheTheoryOfBesselFunctions – Leucippus May 16 '14 at 23:21

0 Answers0