$(p,q)$-Extension of the Whittaker function and its certain properties
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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.
Abstract
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.
참고문헌 (13)
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