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Divided-difference equation, inversion, connection, multiplication and linearization formulae of the continuous Hahn and the Meixner–Pollaczek polynomials

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Abstract

From the study of various properties of some difference operators, we prove in the first part of this work that the continuous Hahn and the Meixner–Pollaczek polynomials are solutions of a second-order divided-difference equation of hypergeometric- type. Next, using some algorithmic tools, we solve the inversion, connection, multiplication and linearization problems for the continuous Hahn and the Meixner–Pollaczek polynomials.

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Acknowledgments

We would like to thank the anonymous referee of this paper for very carefully reading the manuscript, and also for his valuable comments and suggestions which improved the paper significantly.

Author information

Authors and Affiliations

  1. Department of Mathematics, Higher Teachers’ Training College, University of Yaounde I, Cameroon and African Institute for Mathematical Sciences, Limbé, Cameroon

    D. D. Tcheutia & M. Foupouagnigni

  2. Faculty of Industrial Engineering, University of Douala, Douala, Cameroon

    P. Njionou Sadjang

  3. Institute of Mathematics, University of Kassel, Heinrich-Plett Str. 40, 34132, Kassel, Germany

    W. Koepf

Authors
  1. D. D. Tcheutia
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  2. P. Njionou Sadjang
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  3. W. Koepf
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  4. M. Foupouagnigni
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Corresponding author

Correspondence to W. Koepf.

Additional information

This work has been supported by a TWAS / DFG fellowship for P. Njionou Sadjang, the Institute of Mathematics of the University of Kassel (Germany), the 2015–2016 Research Grant of AIMS-Cameroon and a Research-Group Linkage Programme 2009-2012 between the University of Kassel (Germany) and the University of Yaounde I (Cameroon) sponsored by the Alexander von Humboldt Foundation. All these institutions receive our sincere thanks. The computations for this paper were carefully checked with Maple. This Maple file can be downloaded from http://www.mathematik.uni-kassel.de/~koepf/Publikationen/divided_difference_equation_for_CH_and_MP.mw.

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Tcheutia, D.D., Njionou Sadjang, P., Koepf, W. et al. Divided-difference equation, inversion, connection, multiplication and linearization formulae of the continuous Hahn and the Meixner–Pollaczek polynomials. Ramanujan J 45, 33–56 (2018). https://doi.org/10.1007/s11139-016-9870-5

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  • DOI: https://doi.org/10.1007/s11139-016-9870-5

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