대한수학회논문집 (Communications of the Korean Mathematical Society)

  • 제34권4호
  • /
  • Pages.1175-1199
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  • 2019
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  • 1225-1763(pISSN)
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  • 2234-3024(eISSN)
대한수학회 (Korean Mathematical Society)
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A p-DEFORMED q-INVERSE PAIR AND ASSOCIATED POLYNOMIALS INCLUDING ASKEY SCHEME

  • Savalia, Rajesh V. (Research Scholar at Department of Mathematics Faculty of Science The Maharaja Sayajirao University of Baroda)
  • 투고 : 2018.10.07
  • 심사 : 2019.01.04
  • 발행 : 2019.10.31
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초록

We construct a general bi-basic inverse series relation which provides extension to several q-polynomials including the Askey-Wilson polynomials and the q-Racah polynomials. We introduce a general class of polynomials suggested by this general inverse pair which would unify certain polynomials such as the q-extended Jacobi polynomials and q-Konhauser polynomials. We then emphasize on applications of the general inverse pair and obtain the generating function relations, summation formulas involving the associated polynomials and derive the p-deformation of some of the q-analogues of Riordan's classes of inverse series relations. We also illustrate the companion matrix corresponding to the general class of polynomials; this is followed by a chart showing the reducibility of the extended p-deformed Askey-Wilson polynomials as well as the extended p-deformed q-Racah polynomials.

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참고문헌

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