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.
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收藏
页码：795 / 806
页数：12
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