论文标题
明确总结Sneddon-Bessel系列
Summing Sneddon-Bessel series explicitly
论文作者
论文摘要
我们以近距离的形式总和SNEDDON-BESSEL系列\ [\ sum_ {m = 1}^\ infty \ frac {J_α（x J_ {m，n}） j_ {ν+1}（j_ {m，ν}）^2}，\]，其中$ 0 <x $，$ 0 <y $，$ x+y <2 $，$ n $是整数，$α，β，β，ν\ in \ in \ in \ in \ in \ in \ mathbb {C} $ 2 \ operatorName {re}ν<2n+ 1+ \ peratatOrName {re}α+ \ operatorName {re}β$和$ \ {j_ {m，ν} \} _ {m \ geq 0} $是bessel function $ j___ n n n q $ j__nν$ n是bessel function $作为应用程序，我们证明了Kneser-Sommerfeld扩展的一些扩展。
We sum in a close form the Sneddon-Bessel series \[ \sum_{m=1}^\infty \frac{J_α(x j_{m,ν})J_β(y j_{m,ν})} {j_{m,ν}^{2n+α+β-2ν+2} J_{ν+1}(j_{m,ν})^2}, \] where $0<x$, $0<y$, $x+y<2$, $n$ is an integer, $α,β,ν\in \mathbb{C}\setminus \{-1,-2,\dots \}$ with $2\operatorname{Re} ν< 2n+1 + \operatorname{Re} α+ \operatorname{Re} β$ and $\{j_{m,ν}\}_{m\geq 0}$ are the zeros of the Bessel function $J_ν$ of order $ν$. As an application we prove some extensions of the Kneser-Sommerfeld expansion.
