Díaz, Rafael; Pariguan, Eddy On hypergeometric functions and Pochhammer \(k\)-symbol. (English) Zbl 1163.33300 Divulg. Mat. 15, No. 2, 179-192 (2007). The authors introduce the \(k\)-generalized gamma function \(\Gamma_{k}\) which is one parameter determination of the classical gamma function such that \(\lim_{k\to 1}\Gamma_{k}=\Gamma\). Using the similar technique the \(k\)-generalized beta function \(B_{k}\) and the \(k\)-generalized Pochhammer symbol \((x)_{n,k}\) are introduced. Several identities of these new generalizations are established and integral representations for the \(\Gamma_{k}\) and \(B_{k}\) functions are provided. Reviewer: Osman Yürekli (Ithaca) Cited in 3 ReviewsCited in 205 Documents MSC: 33B15 Gamma, beta and polygamma functions 33C47 Other special orthogonal polynomials and functions Keywords:hypergeometric functions; Pochhammer symbol; gamma function; beta function PDFBibTeX XMLCite \textit{R. Díaz} and \textit{E. Pariguan}, Divulg. Mat. 15, No. 2, 179--192 (2007; Zbl 1163.33300) Full Text: arXiv EuDML