×

zbMATH — the first resource for mathematics

Extension of gamma, beta and hypergeometric functions. (English) Zbl 1218.33002
Summary: The main object of this paper is to present generalizations of gamma, beta and hypergeometric functions. Some recurrence relations, transformation formulas, operation formulas and integral representations are obtained for these new generalizations.

MSC:
33B15 Gamma, beta and polygamma functions
PDF BibTeX Cite
Full Text: DOI
References:
[1] Chaudhry, M.A.; Zubair, S.M., Generalized incomplete gamma functions with applications, J. comput. appl. math., 55, 99-124, (1994) · Zbl 0833.33002
[2] Chaudhry, M.A.; Qadir, A.; Rafique, M.; Zubair, S.M., Extension of euler’s beta function, J. comput. appl. math., 78, 19-32, (1997) · Zbl 0944.33003
[3] Chaudhry, M.A.; Zubair, S.M., On the decomposition of generalized incomplete gamma functions with applications to Fourier transforms, J. comput. appl. math., 59, 253-284, (1995) · Zbl 0840.33001
[4] Chaudhry, M.A.; Temme, N.M.; Veling, E.J.M., Asymptotic and closed form of a generalized incomplete gamma function, J. comput. appl. math., 67, 371-379, (1996) · Zbl 0853.33003
[5] Miller, A.R., Reduction of a generalized incomplete gamma function, related kampe de feriet functions, and incomplete Weber integrals, Rocky mountain J. math., 30, 703-714, (2000) · Zbl 0978.33006
[6] AL-Musallam, F.; Kalla, S.L., Futher results on a generalized gamma function occurring in diffraction theory, Integral transforms and spec. funct., 7, 3-4, 175-190, (1998) · Zbl 0922.33001
[7] Chaudhry, M.A.; Zubair, S.M., Extended incomplete gamma functions with applications, J. math. anal. appl., 274, 725-745, (2002) · Zbl 1011.33002
[8] Chaudhry, M.A.; Qadir, A.; Srivastava, H.M.; Paris, R.B., Extended hypergeometric and confluent hypergeometric functions, Appl. math. comput., 159, 589-602, (2004) · Zbl 1067.33001
[9] Andrews, G.E.; Askey, R.; Roy, R., Special functions, (1999), Cambridge University Press Cambridge
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.