Question

$\sum_{n=0}^\infty\frac{H_n(x)H_n(y)t^n}{2^nn!}$=$\frac{\exp\left[\frac{2xyt-(x^2+y^2)t^2}{1-t^2}\right]}{\sqrt{1-t^2}}$

score 143 · Answer 1 · 2026-03-25 05:10:00

143

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$\sum_{n=0}^\infty\frac{H_n(x)H_n(y)t^n}{2^nn!}$=$\frac{\exp\left[\frac{2xyt-(x^2+y^2)t^2}{1-t^2}\right]}{\sqrt{1-t^2}}$

Published on 25 Mar 2026 - 5:10

score 123 · Answer 2 · 2020-05-28 15:40:39

123

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113

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63

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List Question

$\sum_{n=0}^\infty\frac{H_n(x)H_n(y)t^n}{2^nn!}$=$\frac{\exp\left[\frac{2xyt-(x^2+y^2)t^2}{1-t^2}\right]}{\sqrt{1-t^2}}$

Integrate $I=\int_0^{\infty} x^n \, e^{ax+\frac{b}{x}} \, \cos(cx) \, dx$?

A parameterized log-sine integral equating to square of arctan

Special function expression for the (truncated) moment of the generalized Gamma distribution

Definite integral involving hypergeometric functions

How to show that the beta funcction is well defined?

problem about the $\mathscr{E}_1(z)$

Show that $\int_{0}^{\pi/2} (\frac{1}{\sin^3{\theta}} - \frac{1}{\sin^2{\theta}})^{1/4} \cos{\theta} d\theta = \frac{(\Gamma(1/4))^2}{2\sqrt{\pi}}$

Show that $\Gamma(a -S) = \frac{\Gamma(1-a+S)\Gamma(a)}{(-1)^S\Gamma(a-S)}$

Special functions for understanding elemetary integrals

How do you prove that $\ln(x) = \int_0^\infty \frac{e^{-t}-e^{-xt}}{t}$?

Inverse of $C\log x + 1/x$ for $x \in (0,\frac 1 C)$.

Generalised hypergeometric function $_4F_3$ at unit argument

Big-theta asymptotic limit of expression involving incomplete beta function

Mittag-Leffler function for $x$ big

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