INVESTIGADORES
GASANEO Gustavo
artículos
Título:
Derivatives of Horn hypergeometric functions with respect to their parameters
Autor/es:
ANCARANI, L.U.; DEL PUNTA, J.A.; GASANEO, G.
Revista:
JOURNAL OF MATHEMATICAL PHYSICS
Editorial:
AMER INST PHYSICS
Referencias:
Año: 2017 vol. 58
ISSN:
0022-2488
Resumen:
The derivatives of eight Horn hypergeometric functions [four Appell F1, F2, F3, and F4, and four (degenerate) confluent Φ1, Φ2, Ψ1, and Ξ1] with respect to their parameters are studied. The first derivatives are expressed, systematically, as triple infinite summations or, alternatively, as single summations of two-variable Kampé de Fériet functions. Taking advantage of previously established expressions for the derivative of the confluent or Gaussian hypergeometric functions, the generalization to the nth derivative of Horn´s functions with respect to their parameters is rather straightforward in most cases; the results are expressed in terms of n + 2 infinite summations. Following a similar procedure, mixed derivatives are also treated. An illustration of the usefulness of the derivatives of F1, with respect to the first and third parameters, is given with the study of autoionization of atoms occurring as part of a post-collisional process. Their evaluation setting the Coulomb charge to zero provides the coefficients of a Born-like expansion of the interaction.