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In this paper, we obtain a $(p,q)$-extension of the Whittaker function $M_{k,\mu}(z)$ together with its integral representations, by using the extended confluent hypergeometric function of the first kind $\Phi_{p,q}(b;c;z)$ [recently extended by J. Choi]. Also, we give some of its main properties, namely the summation formula, a transformation formula, a Mellin transform, a differential formula and inequalities. In addition, our extension on Whittaker function finds interesting connection with the Laguerre polynomials.
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참고문헌 (13)
참고문헌 신청
M. Abramowitz / 1972 / Handbook of Mathematical Functions / Dover publications
G. E. Andrews / 1999 / Special Functions, Encyclopedia of Mathematics and its Applications / Cambridge University Press :71
M. A. Chaudhry / 1997 / Extension of Euler's beta function / J. Comput. Appl. Math. 78(1):19~32
M. A. Chaudhry / 2004 / Extended hypergeometric and confluent hypergeometric functions / Appl. Math. Comput. 159(2):589~602
J. Choi / 2015 / Generalized extended Whittaker function and its properties / Appl. Math. Sci. 9(131):6529~6541
G. E. Andrews / 1999 / Special Functions, Encyclopedia of Mathematics and its Applications / Cambridge University Press :71
M. A. Chaudhry / 1997 / Extension of Euler's beta function / J. Comput. Appl. Math. 78(1):19~32
M. A. Chaudhry / 2004 / Extended hypergeometric and confluent hypergeometric functions / Appl. Math. Comput. 159(2):589~602
J. Choi / 2015 / Generalized extended Whittaker function and its properties / Appl. Math. Sci. 9(131):6529~6541
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