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 · Sun Jun 15 00:00:00 EDT 2008 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.2939395· OSTI ID:21100324

Ancarani, L U ^[1]; Gasaneo, G ^[2]

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1. Laboratoire de Physique Moleculaire et des Collisions, Universite Paul Verlaine-Metz, 57078 Metz (France)
2. 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, Vol. 49, Issue 6; Other Information: DOI: 10.1063/1.2939395; (c) 2008 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); ISSN 0022-2488
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
HYPERGEOMETRIC FUNCTIONS
INTEGRALS
POWER SERIES
QUANTUM MECHANICS
RECURSION RELATIONS
TWO-BODY PROBLEM
WAVE FUNCTIONS