대한수학회논문집 (Communications of the Korean Mathematical Society)

  • 제33권2호
  • /
  • Pages.619-630
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  • 2018
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  • 1225-1763(pISSN)
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  • 2234-3024(eISSN)
대한수학회 (Korean Mathematical Society)
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(p, q)-EXTENSION OF THE WHITTAKER FUNCTION AND ITS CERTAIN PROPERTIES

  • Dar, Showkat Ahmad (Department of Applied Sciences and Humanities Faculty of Engineering and Technology Jamia Millia Islamia (Central University)) ;
  • Shadab, Mohd (Department of Applied Sciences and Humanities Faculty of Engineering and Technology Jamia Millia Islamia (Central University))
  • 투고 : 2017.02.02
  • 심사 : 2017.11.02
  • 발행 : 2018.04.30
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초록

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

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