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A finite class of q-orthogonal polynomials corresponding to inverse gamma distribution

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Abstract

In this paper, a class of finite q-orthogonal polynomials is studied whose weight function corresponds to the inverse gamma distribution as \(q \rightarrow 1\). Via Sturm–Liouville theory in q-difference spaces, the orthogonality of this class is proved and its norm square value is computed. Also, its general properties such as q-weight function, q-difference equation and the basic hypergeometric representation are recovered in the continuous case.

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Acknowledgments

The authors thank the reviewer for helpful suggestions and comments as well as for bringing out to our attention the Reference [9].

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Authors and Affiliations

  1. Department of Mathematics, K.N. Toosi University of Technology, P.O. Box 16315–1618, Tehran, Iran

    F. Soleyman & M. Masjed-Jamei

  2. Departamento de Matemática Aplicada II, E.E. Aeronáutica e do Espazo, Campus As Lagoas s/n, Universidade de Vigo, 32004, Ourense, Spain

    I. Area

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  1. F. Soleyman
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  2. M. Masjed-Jamei
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  3. I. Area
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Correspondence to I. Area.

Additional information

The work of I. Area has been partially supported by the Ministerio de Ciencia e Innovación of Spain under grant MTM2012–38794–C02–01, co-financed by the European Community fund FEDER.

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Soleyman, F., Masjed-Jamei, M. & Area, I. A finite class of q-orthogonal polynomials corresponding to inverse gamma distribution. Anal.Math.Phys. 7, 479–492 (2017). https://doi.org/10.1007/s13324-016-0150-8

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  • DOI: https://doi.org/10.1007/s13324-016-0150-8

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