Navegar

Colección

Datos Estadísticas

Artículo

El editor solo permite decargar el artículo en su versión post-print desde el repositorio. Por favor, si usted posee dicha versión, enviela a
Consulte el artículo en la página del editor
Consulte la política de Acceso Abierto del editor

Abstract:

In this work we present a numerical scheme to compute the two-variable hypergeometric function F1(α, β, β′, γ; x, y) of Appell for complex parameters α, β, β′ and γ, and real values of the variables x and y. We implement a set of analytic continuations that allow us to obtain the F1 function outside the region of convergence of the series definition. These continuations can be written in terms of the Horn's G2 function, Appell's F2 function related, and the F1 hypergeometric itself. The computation of the function inside the region of convergence is achieved by two complementary methods. The first one involves a single-index series expansion of the F1 function, while the second one makes use of a numerical integration of a third order ordinary differential equation that represents the system of partial differential equations of the F1 function. We briefly sketch the program and show some examples of the numerical computation. © 2001 Elsevier Science B.V.

Registro:

Documento: Artículo
Título:Numerical evaluation of Appell's F1 hypergeometric function
Autor:Colavecchia, F.D.; Gasaneo, G.; Miraglia, J.E.
Filiación:Centro Atómico Bariloche, Consejo Nacional De Investigaciones Científicas Y Técnicas, 8400 S.C. de Bariloche, Argentina
Departmento De Física, Universidad Nacional del Sur, Av. Alem 1453, 8000 Bahía Blanca, Argentina
Instituto De Física Y Astronomía del Espacio, Consejo Nacional De Investigaciones Científicas Y Técnicas, 1428 Buenos Aires, Argentina
Theoretical Division (T-12, MS B268), Los Alamos National Laboratory, Los Alamos, NM 87545, United States
Palabras clave:Appell functions; Gauss function; Hypergeometric functions; Numerical methods; Special functions; Computational complexity; Computational geometry; Convergence of numerical methods; Integration; Ordinary differential equations; Partial differential equations; Appell's function; Horn's function; Hypergeometric functions; Function evaluation
Año:2001
Volumen:138
Número:1
Página de inicio:29
Página de fin:43
DOI: http://dx.doi.org/10.1016/S0010-4655(01)00186-2
Título revista:Computer Physics Communications
Título revista abreviado:Comput Phys Commun
ISSN:00104655
CODEN:CPHCB
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00104655_v138_n1_p29_Colavecchia

Referencias:

  • Press, W.H., Teulkolsky, S.A., Vetterling, W.T., Flannery, B.P., (1996) Numerical Recipes in Fortran 77, , Cambridge University Press, New York, Chapters 5 and 6
  • Gradshteyn, I.S., Ryzhik, I.M., (1980) Table of Integrals, Series and Products, , Academic Press Inc., Orlando
  • Forrey, R.C., (1997) J. Comput. Phys., 137, p. 79
  • Bess, L., (1949) Phys. Rev., 77, p. 550
  • Nordsieck, A., (1954) Phys. Rev., 93, p. 785
  • Gravielle, M.S., Miraglia, J.E., (1992) Comput. Phys. Comm., 69, p. 53
  • Colavecchia, F.D., Gasaneo, G., Garibotti, C.R., (1997) J. Math. Phys., 38, p. 6603
  • Appell, P., Kampé de Feriet, J., (1926) Fonctions Hypergéométriques et Hypersphériques Polynômes d'Hermite, , Gauthier-Villars, Paris
  • Colavecchia, F.D., Gasaneo, G., Garibotti, C.R., (2000) J. Phys. B: At. Mol. Opt. Phys., 33, pp. L467
  • Le Vavasseur, M.R., (1893) Thèses, , Gauthier-Villars, Paris
  • Erdelyi, A., (1950) Acta Mat., 83, p. 131
  • Horn, J., (1931) Math. Ann., 105, p. 381
  • Olsson, P.O.M., (1964) J. Math. Phys., 5, p. 420
  • (1953) Higher Trascendental Functions, 1, p. 222. , A. Erdelyi (Ed.), McGraw-Hill, New York
  • Burchnall, J.L., (1942) Quart. J. Math. (Oxford), 13, p. 90
  • Burchnall, J.L., Chaundy, T.W., (1940) Quart. J. Math. (Oxford), 11, p. 248
  • Burchnall, J.L., Chaundy, T.W., (1941) Quart. J. Math. (Oxford), 12, p. 112

Citas:

---------- APA ----------
Colavecchia, F.D., Gasaneo, G. & Miraglia, J.E. (2001) . Numerical evaluation of Appell's F1 hypergeometric function. Computer Physics Communications, 138(1), 29-43.
http://dx.doi.org/10.1016/S0010-4655(01)00186-2
---------- CHICAGO ----------
Colavecchia, F.D., Gasaneo, G., Miraglia, J.E. "Numerical evaluation of Appell's F1 hypergeometric function" . Computer Physics Communications 138, no. 1 (2001) : 29-43.
http://dx.doi.org/10.1016/S0010-4655(01)00186-2
---------- MLA ----------
Colavecchia, F.D., Gasaneo, G., Miraglia, J.E. "Numerical evaluation of Appell's F1 hypergeometric function" . Computer Physics Communications, vol. 138, no. 1, 2001, pp. 29-43.
http://dx.doi.org/10.1016/S0010-4655(01)00186-2
---------- VANCOUVER ----------
Colavecchia, F.D., Gasaneo, G., Miraglia, J.E. Numerical evaluation of Appell's F1 hypergeometric function. Comput Phys Commun. 2001;138(1):29-43.
http://dx.doi.org/10.1016/S0010-4655(01)00186-2