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On the Relation between Pincherle's Polynomials and the Hypergeometric Function

Published online by Cambridge University Press:  20 January 2009

Bevan B. Baker
Bevan B. Baker
Affiliation:
Lecturer in Mathematics in the University of Edinburgh
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1. The Pincherle polynomials are defined as the coefficients in the expansion of {1 − 3 tx + t3}−½ in ascending powers of t. If the coefficient of tn be denoted by Pn(x), then the polynomials satisfy the difference equation

and Pn(x) satisfies the differential equation

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 39 , February 1920 , pp. 58 - 62
Copyright
Copyright © Edinburgh Mathematical Society 1920

References

* Pincherle, S.. Mem. della R. Accad. di Bologna, S. 5, T. I. (1890), p. 337Google Scholar

† Humbert, , Proc. Edin. Math. Soc., (1921).Google Scholar