An extension of some hypergeometric functions of two variables

• Autores: A. H. Al-Shammery, S. L. Kalla
• Localización: Revista de la Academia Canaria de Ciencias: = Folia Canariensis Academiae Scientiarum, ISSN 1130-4723, Vol. 12, Nº. 1-2, 2000, págs. 189-196
• Idioma: inglés
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• Resumen

  • Recently, Vircbenko et al. [ Fract Cale. Appl. Anal. Vol. 2, No. 3 (1999), 233-244; Integral Transform. Spect Funct, Vol. 10 (2001)] have extended Gauss' hypergeometric function by introducing an additional parameter r. This paper deals with extension of Appell's bypergeometric · functions (F,,i = 1,2,3) and the confluent hpergeometric functions (cJ.>1,i = 1,.2,3) oftwo variables.

    These functions are defined by their series representations and corresponding integral representations are establisbed. Sorne identities involving these functions are listed, and sorne special cases are mentioned.