Inverse Laplace transforms of products of Whittaker functions

被引：0

作者：

Beals, Richard ^{[1
]}

Kannai, Yakar ^{[2
]}

机构：

[1] Yale Univ, Dept Math, New Haven, CT 06520 USA

[2] Weizmann Inst Sci, Dept Math, IL-76100 Rehovot, Israel

来源：

PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES | 2008年 / 464卷 / 2092期

关键词：

Kummer functions; Whittaker functions; Laplace transform;

D O I：

10.1098/rspa.2007.0248

中图分类号：

O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];

学科分类号：

07 ; 0710 ; 09 ;

摘要：

Identities of the form W-1(z)W-2(zeta) = integral(infinity)(0) e(-r)g(z,zeta,T)dr are proved. Here W-1 is either of the Whittaker functions W-k,W-mu or M-k,M-mu and W-2 is either ofW(K',mu) or M-K',M--mu. The function g has, piecewise, a form that involves a hypergeometric function of a rational function of z and zeta. These identities make possible the calculation of explicit global propagators for certain singular hyperbolic equations and degenerate hyperbolic equations in two variables of the form x(2k-2)u(yy)+lambda(k-1)x(k-2)u(y)-u(xx) = 0.

引用

页码：795 / 806

页数：12