Abstract
It is shown how symbolic computer algebraic systems such as Mathematica, Macsyma, SMP, etc., can be used to derive transformation and expansion formulas for orthogonal polynomials that are expressible in terms of either hypergeometric or basic hypergeometric series. In particular, we demonstrate how Mathematica can be used to apply transformation formulas to the Racah and q-Racah polynomials, to derive an indefinite bibasic summation formula, an expansion formula for Laguerre polynomials, Clausen’s formula for the square of hypergeometric series, a q-analogue of a Fields and Wimp expansion formula, and to prove the Askey-Gasper inequality which de Branges used in his proof of the Bieberbach conjecture. We also make some observations and conjectures related to Jensen’s necessary and sufficient conditions for the Riemann Hypothesis to hold.
This material is based upon research supported in part by the National Science Foundation under grant number DMS-8601901.
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© 1990 Kluwer Academic Publishers
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Gasper, G. (1990). Using Symbols Computer Algebraic Systems to Derive Formulas Involving Orthogonal Polynomials and Other Special Functions. In: Nevai, P. (eds) Orthogonal Polynomials. NATO ASI Series, vol 294. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-0501-6_8
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DOI: https://doi.org/10.1007/978-94-009-0501-6_8
Publisher Name: Springer, Dordrecht
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