On an extension of extended beta and hypergeometric functions
Copyright policy )On an extension of extended beta and hypergeometric functions
Motivated mainly by certain interesting recent extensions of the Gamma, Beta and hypergeometric functions, we introduce here new extensions of the Beta function, hypergeometric and confluent hypergeometric functions. We systematically investigate several properties of each of these extended functions, namely their various integral representations, Mellin transforms, derivatives, transformations, summation formulas and asymptotics. Relevant connections of certain special cases of the main results presented here are also pointed out.
14 pages, 0 figures
- University of Abertay Dundee United Kingdom
Generalized hypergeometric series, \({}_pF_q\), extended beta function, Incomplete beta and gamma functions (error functions, probability integral, Fresnel integrals), transformation formulas, summation formula, extended gamma function, extended confluent hypergeometric function, Mellin transforms, generalized gamma function, Classical hypergeometric functions, \({}_2F_1\), Mathematics - Classical Analysis and ODEs, Classical Analysis and ODEs (math.CA), FOS: Mathematics, extended hypergeometric function, 33B20, 33C20, 33B15, 33C05, Gamma, beta and polygamma functions
Generalized hypergeometric series, \({}_pF_q\), extended beta function, Incomplete beta and gamma functions (error functions, probability integral, Fresnel integrals), transformation formulas, summation formula, extended gamma function, extended confluent hypergeometric function, Mellin transforms, generalized gamma function, Classical hypergeometric functions, \({}_2F_1\), Mathematics - Classical Analysis and ODEs, Classical Analysis and ODEs (math.CA), FOS: Mathematics, extended hypergeometric function, 33B20, 33C20, 33B15, 33C05, Gamma, beta and polygamma functions
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