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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.
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참고문헌 (16)
참고문헌 신청
Y. A. Brychkov / 2008 / Handbook of Special Functions (Derivatives, Integrals, Series and Other Formulas) / Taylor & Francis Group, LLC; Chapman & Hall/CRC
M. A. Chaudhry / 1997 / Extension of Euler's Beta function / J. Comput. Appl. Math 78:19~32
M. A. Chaudhry / 2004 / Extended hy-pergeometric and con uent hypergeometric functions / Appl. Math. Comput 159:589~602
M. A. Chaudhry / 1996 / Asymptotic and closed form of a generalized incomplete gamma function / J. Comput. Appl. Math 67:371~379
M. A. Chaudhry / 1994 / Generalized incomplete gamma functions with applications / J. Comput. Appl. Math 55:99~124
M. A. Chaudhry / 1997 / Extension of Euler's Beta function / J. Comput. Appl. Math 78:19~32
M. A. Chaudhry / 2004 / Extended hy-pergeometric and con uent hypergeometric functions / Appl. Math. Comput 159:589~602
M. A. Chaudhry / 1996 / Asymptotic and closed form of a generalized incomplete gamma function / J. Comput. Appl. Math 67:371~379
M. A. Chaudhry / 1994 / Generalized incomplete gamma functions with applications / J. Comput. Appl. Math 55:99~124
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