Take the 2-minute tour ×
MathOverflow is a question and answer site for professional mathematicians. It's 100% free, no registration required.

¿Could somebody tell me how can i write a zero order bessel function in an Hermite-Gauss basis? Thanks

share|improve this question
add comment

2 Answers 2

up vote 2 down vote accepted

The Hermite-Gauss functions (suitably normalized) are orthonormal for an inner product defined by integration, just like $\{\sin(nx),\cos(mx)\}$ as $n,m$ run over positive integers. The coefficients of an expansion of a $J$-Bessel function in terms of Hermite-Gauss functions are computed by integrating the Bessel functions against the various Hermite-Gauss functions, in a way analogous to how a Fourier expansion is computed. You'll want to be looking at a table of integrals, or maybe Mathematica. (I'm not guaranteeing anything about the convergence of the series; I haven't thought about it that much.)

share|improve this answer
add comment

Thank you very much! I was thinking in an expansion tabulated yet like those appearing in Gradstein and Ryzhik, but i didn't find it anywhere.

share|improve this answer
See also en.wikipedia.org/wiki/Hermite_polynomials#Hermite_functions for details –  Stopple Oct 21 '10 at 21:26
add comment

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.