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Artículo

Derivatives of Horn hypergeometric functions with respect to their parameters

Ancarani, L. U.; del Punta, Jessica AdrianaIcon ; Gasaneo, GustavoIcon
Fecha de publicación: 24/07/2017
Editorial: American Institute of Physics
Revista: Journal of Mathematical Physics
ISSN: 0022-2488
Idioma: Inglés
Tipo de recurso: Artículo publicado
Clasificación temática:
Matemática Pura

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.
Palabras clave: Horn Hypergeometric Functions , Derivatives , Parameters
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info:eu-repo/semantics/openAccess Excepto donde se diga explícitamente, este item se publica bajo la siguiente descripción: Creative Commons Attribution-NonCommercial-ShareAlike 2.5 Unported (CC BY-NC-SA 2.5)
Identificadores
URI: http://hdl.handle.net/11336/64180
DOI: http://dx.doi.org/10.1063/1.4994059
URL: https://aip.scitation.org/doi/10.1063/1.4994059
URL: https://arxiv.org/abs/1712.07579
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Articulos(IFISUR)
Articulos de INSTITUTO DE FISICA DEL SUR
Citación
Ancarani, L. U.; del Punta, Jessica Adriana; Gasaneo, Gustavo; Derivatives of Horn hypergeometric functions with respect to their parameters; American Institute of Physics; Journal of Mathematical Physics; 58; 7; 24-7-2017; 1-18; 073504
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