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Orthogonal polynomials and continued fractions arising from contiguous relations and generalizations of Kummer and q-Kummer identities

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Abstract

In this paper, we show formally how can we generate continued fractions starting from three-term contiguous relations. Then as examples, starting from certain contiguous relations for \({}_2F_1\) and \({}_2\phi _1\), we derive orthogonal polynomials, continued fractions and in case of \({}_2F_1\), the measure of orthogonality. Also, a generalization of q-Kummer’s identity is introduced.

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Acknowledgements

I would like to thank professor Mourad Ismail for bringing this research point to my attention, and for his helpful comments and support.

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Correspondence to Zeinab S. I. Mansour.

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Mansour, Z.S.I. Orthogonal polynomials and continued fractions arising from contiguous relations and generalizations of Kummer and q-Kummer identities. Ramanujan J 49, 353–369 (2019). https://doi.org/10.1007/s11139-018-0015-x

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  • DOI: https://doi.org/10.1007/s11139-018-0015-x

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