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The Ramanujan Journal

, Volume 45, Issue 1, pp 33–56 | Cite as

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

  • D. D. Tcheutia
  • P. Njionou Sadjang
  • W. KoepfEmail author
  • M. Foupouagnigni
Article

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.

Keywords

Meixner–Pollaczek polynomials Continuous Hahn polynomials Divided-difference equations Inversion formula Connection formula Multiplication formula Linearization formula 

Mathematics Subject Classification

33C05 33C45 33F10 39A13 

Notes

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.

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Copyright information

© Springer Science+Business Media New York 2017

Authors and Affiliations

  • D. D. Tcheutia
    • 1
  • P. Njionou Sadjang
    • 2
  • W. Koepf
    • 3
    Email author
  • M. Foupouagnigni
    • 1
  1. 1.Department of Mathematics, Higher Teachers’ Training CollegeUniversity of Yaounde I, Cameroon and African Institute for Mathematical SciencesLimbéCameroon
  2. 2.Faculty of Industrial EngineeringUniversity of DoualaDoualaCameroon
  3. 3.Institute of MathematicsUniversity of KasselKasselGermany

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