Inverse Laplace transforms of products of Whittaker functions

Richard Beals; Yakar Kannai

doi:10.1098/rspa.2007.0248

Inverse Laplace transforms of products of Whittaker functions

Richard Beals
, Yakar Kannai

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

Identities of the formW₁(z)W₂(ζ)=₀e^{- τ}g(z,ζ,τ)dτare proved. Here W₁ is either of the Whittaker functions W_κ,μ or M_κ,μ and W₂ is either of W_κ′,μor M_{κ ′,-μ}. The function g has, piecewise, a form that involves a hypergeometric function of a rational function of z and ζ. These identities make possible the calculation of explicit global propagators for certain singular hyperbolic equations and degenerate hyperbolic equations in two variables of the formx^2K-2u_yy+λ(k-1)x^k-2u_y-u_xx=0

Original language	English
Pages (from-to)	795-806
Number of pages	12
Journal	Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Volume	464
Issue number	2092
DOIs	https://doi.org/10.1098/rspa.2007.0248
State	Published - 8 Apr 2008
Externally published	Yes

Keywords

Kummer functions
Laplace transform
Whittaker functions

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10.1098/rspa.2007.0248

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abstract = "Identities of the formW1(z)W2(ζ)=0e- τg(z,ζ,τ)dτare proved. Here W1 is either of the Whittaker functions Wκ,μ or Mκ,μ and W2 is either of Wκ′,μor Mκ ′,-μ. The function g has, piecewise, a form that involves a hypergeometric function of a rational function of z and ζ. These identities make possible the calculation of explicit global propagators for certain singular hyperbolic equations and degenerate hyperbolic equations in two variables of the formx2K-2uyy+λ(k-1)xk-2uy-uxx=0",

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AU - Beals, Richard

AU - Kannai, Yakar

PY - 2008/4/8

Y1 - 2008/4/8

N2 - Identities of the formW1(z)W2(ζ)=0e- τg(z,ζ,τ)dτare proved. Here W1 is either of the Whittaker functions Wκ,μ or Mκ,μ and W2 is either of Wκ′,μor Mκ ′,-μ. The function g has, piecewise, a form that involves a hypergeometric function of a rational function of z and ζ. These identities make possible the calculation of explicit global propagators for certain singular hyperbolic equations and degenerate hyperbolic equations in two variables of the formx2K-2uyy+λ(k-1)xk-2uy-uxx=0

AB - Identities of the formW1(z)W2(ζ)=0e- τg(z,ζ,τ)dτare proved. Here W1 is either of the Whittaker functions Wκ,μ or Mκ,μ and W2 is either of Wκ′,μor Mκ ′,-μ. The function g has, piecewise, a form that involves a hypergeometric function of a rational function of z and ζ. These identities make possible the calculation of explicit global propagators for certain singular hyperbolic equations and degenerate hyperbolic equations in two variables of the formx2K-2uyy+λ(k-1)xk-2uy-uxx=0

KW - Kummer functions

KW - Laplace transform

KW - Whittaker functions

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JF - Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

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ER -

Inverse Laplace transforms of products of Whittaker functions

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Keywords

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