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1. ### Hermite Polynomial identity

Does anyone know how to prove the following identity: \Sigma_{k=0}^{n}\left(\stackrel{n}{k}\right) H_{k}(x)H_{n-k}(y)=2^{n/2}H_{n}(2^{-1/2}(x+y)) where H_{i}(z)represents the Hermite polynomial?
2. ### Solution to an exponential integral

Hi, I am trying to find an analytic solution to the following double integral...
3. ### Exponential integral with trigonometric argument

Hi, Does anyone know of an analytic solution for the integral \int_{0}^{\pi}\sin\theta\exp\left(a\sin^{2}\theta+b\sin\theta\right)d\theta Thanks.
4. ### Proof of a definite multiple integral relation

Hello, The following is identity no. 4.624 in Gradshteyn & Ryzhik's Table of Integrals, Series and Products: \int_0^{\pi}\int_0^{2\pi}f\left(\alpha\cos\theta+\beta\sin\theta\cos\phi+\gamma\sin\theta\sin\phi\right)\sin\theta d\theta d\phi=2\pi\int_0^{\pi}f\left(R\cos...
5. ### Integrating products of Bessel functions

Hi guys, Does anyone have any ideas about an analytical solution for the following integral? \int_{0}^{2\pi}J_{m}\left(z_{1}\cos\theta\right)J_{n}\left(z_{2}\sin\theta\right)d\theta J_{m}\left(\right) is a Bessel function of the first kind of order m. Thanks.
6. ### Analytic solution to an exponential integral

Hello, I am trying to find an analytic solution to the following: \int_{-1}^{1}\exp(-p\sqrt{1-x^{2}}-qx)dx where p,q > 0. Does anyone have any ideas? Thanks.