An extension of Pochhammer’s symbol and its application to hypergeometric functions
Copyright policy )An extension of Pochhammer’s symbol and its application to hypergeometric functions
By using a special property of the gamma function, we first define a productive form of gamma and beta functions and study some of their general properties in order to define a new extension of the Pochhammer symbol. We then apply this extended symbol for generalized hypergeometric series and study the convergence problem with some illustrative examples in this sense. Finally, we introduce two new extensions of Gauss and confluent hypergeometric series and obtain some of their general properties.
- University of Niš Serbia
- Serbian Academy of Sciences and Arts Serbia
- K.N.Toosi University of Technology Iran (Islamic Republic of)
gamma and beta functions, Generalized hypergeometric series, \({}_pF_q\), Convergence and divergence of series and sequences of functions, incomplete gamma, Gauss and confluent hypergeometric functions, Pochhammer symbol, additive form of gamma, Classical hypergeometric functions, \({}_2F_1\), beta and incomplete beta functions, generalized hypergeometric functions, Gauss and confluent hypergeometric series, convergence radius, Confluent hypergeometric functions, Whittaker functions, \({}_1F_1\), Gamma, beta and polygamma functions, generalized hypergeometric series
gamma and beta functions, Generalized hypergeometric series, \({}_pF_q\), Convergence and divergence of series and sequences of functions, incomplete gamma, Gauss and confluent hypergeometric functions, Pochhammer symbol, additive form of gamma, Classical hypergeometric functions, \({}_2F_1\), beta and incomplete beta functions, generalized hypergeometric functions, Gauss and confluent hypergeometric series, convergence radius, Confluent hypergeometric functions, Whittaker functions, \({}_1F_1\), Gamma, beta and polygamma functions, generalized hypergeometric series
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