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

1 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

Access to Document

10.1098/rspa.2007.0248

Cite this

@article{10c81f87df4b4fcb848c4bdc78403b0d,

title = "Inverse Laplace transforms of products of Whittaker functions",

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",

keywords = "Kummer functions, Laplace transform, Whittaker functions",

author = "Richard Beals and Yakar Kannai",

year = "2008",

month = apr,

day = "8",

doi = "10.1098/rspa.2007.0248",

language = "אנגלית",

volume = "464",

pages = "795--806",

journal = "Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences",

issn = "1364-5021",

publisher = "The Royal Society",

number = "2092",

}

TY - JOUR

T1 - Inverse Laplace transforms of products of Whittaker functions

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

UR - http://www.scopus.com/inward/record.url?scp=39449134604&partnerID=8YFLogxK

U2 - 10.1098/rspa.2007.0248

DO - 10.1098/rspa.2007.0248

M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???

AN - SCOPUS:39449134604

SN - 1364-5021

VL - 464

SP - 795

EP - 806

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

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

IS - 2092

ER -

Inverse Laplace transforms of products of Whittaker functions

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this