Derivatives of any order of the confluent hypergeometric function {sub 1}F{sub 1}(a,b,z) with respect to the parameter a or b
Journal Article
·
· Journal of Mathematical Physics
- Laboratoire de Physique Moleculaire et des Collisions, Universite Paul Verlaine-Metz, 57078 Metz (France)
- Departamento de Fisica, Universidad Nacional del Sur and Consejo Nacional de Investigaciones Cientificas y Tecnicas, 8000 Bahia Blanca, Buenos Aires (Argentina)
The derivatives to any order of the confluent hypergeometric (Kummer) function F={sub 1}F{sub 1}(a,b,z) with respect to the parameter a or b are investigated and expressed in terms of generalizations of multivariable Kampe de Feriet functions. Various properties (reduction formulas, recurrence relations, particular cases, and series and integral representations) of the defined hypergeometric functions are given. Finally, an application to the two-body Coulomb problem is presented: the derivatives of F with respect to a are used to write the scattering wave function as a power series of the Sommerfeld parameter.
- OSTI ID:
- 21100324
- Journal Information:
- Journal of Mathematical Physics, Journal Name: Journal of Mathematical Physics Journal Issue: 6 Vol. 49; ISSN JMAPAQ; ISSN 0022-2488
- Country of Publication:
- United States
- Language:
- English
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