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
收藏
页码：795 / 806
页数：12
相关论文
共 50 条
  • [1] INVERSE LAPLACE TRANSFORMS FOR PERIODIC FUNCTIONS
    RUBIN, IS
    ELECTRONIC ENGINEER, 1968, 27 (10): : 74 - &
  • [2] INVERSE LAPLACE TRANSFORM OF PRODUCT OF BESSEL AND WHITTAKER FUNCTIONS
    RATHIE, PN
    JOURNAL OF THE LONDON MATHEMATICAL SOCIETY, 1965, 40 (158P): : 367 - &
  • [3] INVERSE LAPLACE TRANSFORM OF PRODUCT OF 2 WHITTAKER FUNCTIONS
    RAGAB, FM
    PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY, 1962, 58 (OCT): : 580 - &
  • [4] Inverse Laplace transforms of luminescence relaxation functions
    Berberan-Santos, Mario N.
    ADVANCES IN COMPUTATIONAL METHODS IN SCIENCES AND ENGINEERING 2005, VOLS 4 A & 4 B, 2005, 4A-4B : 70 - 73
  • [5] NORMALIZATION OF INVERSE LAPLACE TRANSFORMS FOR RATIONAL FUNCTIONS
    ALBERTOS, P
    ARACIL, R
    ALVAREZ, M
    REVUE FRANCAISE D AUTOMATIQUE INFORMATIQUE RECHERCHE OPERATIONNELLE, 1976, 10 (04): : 103 - 109
  • [6] Index transforms associated with products of Whittaker's functions
    Yakubovich, SB
    JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2002, 148 (02) : 419 - 427
  • [7] Inverse Laplace Transforms of the Fractional Order Transfer Functions
    Yuce, Ali
    Tan, Nusret
    2019 11TH INTERNATIONAL CONFERENCE ON ELECTRICAL AND ELECTRONICS ENGINEERING (ELECO 2019), 2019, : 775 - 779
  • [8] MELLIN TRANSFORMS OF WHITTAKER FUNCTIONS
    FRIEDBERG, S
    GOLDFELD, D
    BULLETIN DE LA SOCIETE MATHEMATIQUE DE FRANCE, 1993, 121 (01): : 91 - 107
  • [9] Mellin transforms of Whittaker functions
    Deitmar, A
    CANADIAN MATHEMATICAL BULLETIN-BULLETIN CANADIEN DE MATHEMATIQUES, 2002, 45 (03): : 364 - 377
  • [10] Squared radial Ornstein-Uhlenbeck processes and inverse Laplace transforms of products of confluent hypergeometric functions
    Moslehi, Leila
    Ansari, Alireza
    HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS, 2017, 46 (03): : 409 - 417
12345