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The Ramanujan Journal

, Volume 48, Issue 1, pp 217–231 | Cite as

Nonnegative linearization coefficients of the generalized Bessel polynomials

  • D. D. TcheutiaEmail author
Article
  • 86 Downloads

Abstract

In this work, we solve the general linearization problem for the generalized Bessel polynomials using their inversion formula. For some particular values, we get a recurrence relation satisfied by the linearization coefficients from which we deduce their nonnegativity. We also recover a result given by Berg and Vignat (Constr Approx 27:15–32, 2008) and derived an explicit formula that generalizes a result by Atia and Zeng (Ramanujan J 28:211–221, 2012).

Keywords

Linearization formula Multiplication formula Bessel polynomials Nonnegativity 

Mathematics Subject Classification

33C10 33C45 

Notes

Acknowledgements

The author is grateful for the useful comments from the referee which improve considerably this manuscript.

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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Institute of MathematicsUniversity of KasselKasselGermany

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