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?
Hello,
The following is identity no. 4.624 in Gradshteyn & Ryzhik's Table of Integrals, Series and Products:
\begin{equation}
\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...
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.
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.