Extensions of the Kummer evaluation of a finite hypergeometric series

Extensions of the Kummer evaluation of a finite hypergeometric series

Kummer's evaluation of a finite hypergeometric series F ( a , b ; c ; - 1 ) ( c = b - a + 1 , b = - 2 m ) is extended in two directions to answer questions related to the positivity of Jost functions arising from one-dimensional Schrödinger equations with exponentially decaying potentials.

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Veröffentlicht in:Journal of computational and applied mathematics 2006-09, Vol.194 (1), p.131-140
Hauptverfasser: Brown, B.M., Eastham, M.S.P.
Format: Artikel
Sprache:eng
Schlagworte:
Exact sciences and technology
Jost function
Mathematical analysis
Mathematics
Partial differential equations
Sciences and techniques of general use
Special functions
Spectral theory
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Zusammenfassung:Kummer's evaluation of a finite hypergeometric series F ( a , b ; c ; - 1 ) ( c = b - a + 1 , b = - 2 m ) is extended in two directions to answer questions related to the positivity of Jost functions arising from one-dimensional Schrödinger equations with exponentially decaying potentials.
ISSN:0377-0427
1879-1778
DOI:10.1016/j.cam.2005.06.018