Abstract
In this article, some new linearization formulae of products of Jacobi polynomials for certain parameters are derived. These new derived formulae are expressed in terms of hypergeometric functions of unit argument, and they generalize some existing formulae in the literature. With the aid of some standard formulae and also by employing symbolic algebraic computation, and in particular Zeilberger’s algorithm, several reduction formulae for summing certain terminating hypergeometric functions of unit argument are given, and hence several linearization formulae of products of Jacobi polynomials for special parameters free of hypergeometric functions are deduced.
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The authors would like to thank the anonymous referees for their valuable and constructive comments which improved the manuscript in its present form.
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Abd-Elhameed, W.M., Doha, E.H. & Ahmed, H.M. Linearization formulae for certain Jacobi polynomials. Ramanujan J 39, 155–168 (2016). https://doi.org/10.1007/s11139-014-9668-2
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DOI: https://doi.org/10.1007/s11139-014-9668-2
Keywords
- Jacobi polynomials
- Linearization problems
- Generalized hypergeometric functions
- Algorithms by Zeilberger, Petkovsek and van Hoeij