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EXTENSION OF EXTENDED BETA, HYPERGEOMETRIC AND CONFLUENT HYPERGEOMETRIC FUNCTIONS

  • Choi, Junesang ;
  • Rathie, Arjun K. ;
  • Parmar, Rakesh K.
  • Received : 2014.03.13
  • Accepted : 2014.04.23
  • Published : 2014.06.25

Abstract

Recently several authors have extended the Gamma function, Beta function, the hypergeometric function, and the confluent hypergeometric function by using their integral representations and provided many interesting properties of their extended functions. Here we aim at giving further extensions of the abovementioned extended functions and investigating various formulas for the further extended functions in a systematic manner. Moreover, our extension of the Beta function is shown to be applied to Statistics and also our extensions find some connections with other special functions and polynomials such as Laguerre polynomials, Macdonald and Whittaker functions.

Keywords

Gamma function;Beta function;hypergeometric function;extended Beta function;extended hypergeometric function;extended confluent hypergeometric function;Mellin transform;summation formula

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  3. A comparative study on generating function relations for generalized hypergeometric functions via generalized fractional operators vol.2018, pp.1, 2018, https://doi.org/10.1186/s13662-018-1612-0