Formula:KLS:09.15:14

<< Formula:KLS:09.15:13

formula in Hermite

Formula:KLS:09.15:15 >>

${\displaystyle{\displaystyle{\displaystyle{\mathrm{e}^{-t^{2}}}\cosh\left(2xt\right)=\sum_{n=0}^{\infty}\frac{H_{2n}\left(x\right)}{(2n)!}t^{2n}}}}$

Proof

We ask users to provide proof(s), reference(s) to proof(s), or further clarification on the proof(s) in this space.

Symbols List

${\displaystyle{\displaystyle{\displaystyle\mathrm{e}}}}$ : the base of the natural logarithm : http://dlmf.nist.gov/4.2.E11
${\displaystyle{\displaystyle{\displaystyle\mathrm{cosh}}}}$ : hyperbolic cosine function : http://dlmf.nist.gov/4.28#E2
${\displaystyle{\displaystyle{\displaystyle\Sigma}}}$ : sum : http://drmf.wmflabs.org/wiki/Definition:sum
${\displaystyle{\displaystyle{\displaystyle H_{n}}}}$ : Hermite polynomial ${\displaystyle{\displaystyle{\displaystyle H_{n}}}}$ : http://dlmf.nist.gov/18.3#T1.t1.r28

Bibliography

Equation in Section 9.15 of KLS.

URL links

We ask users to provide relevant URL links in this space.

<< Formula:KLS:09.15:13

formula in Hermite

Formula:KLS:09.15:15 >>