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Extension of gamma, beta and hypergeometric functions

✍ Scribed by Emine Özergin; Mehmet Ali Özarslan; Abdullah Altın

Publisher
Elsevier Science
Year
2011
Tongue
English
Weight
236 KB
Volume
235
Category
Article
ISSN
0377-0427

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✦ Synopsis

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.

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✍ E.A Karatsuba; M Vuorinen 📂 Article 📅 2001 🏛 Elsevier Science 🌐 English ⚖ 118 KB

We prove some convexity properties for a sum of hypergeometric functions and obtain a generalization of Legendre's relation for complete elliptic integrals. We apply these results to prove some inequalities for hypergeometric functions, incomplete beta-functions, and Legendre functions.