Hostname: page-component-cd9895bd7-8ctnn Total loading time: 0 Render date: 2024-12-24T12:23:24.628Z Has data issue: false hasContentIssue false
  • English
  • Français

Infinite sets of identities for classical polynomials and Bessel functions

Published online by Cambridge University Press:  24 October 2008

Mostafa A. Abdelkader
Mostafa A. Abdelkader
Affiliation:
25, Sh. Champollion, Alexandria, Egypt
Get access Rights & Permissions [Opens in a new window]

Abstract

An identity for a rational function is used, in conjunction with generating functions for a certain class of polynomials, to derive infinite sets of identities for these polynomials. Identities are given for the polynomials of Legendre, Gegenbauer, Hermite, Tchebycheff and L. Carlitz. A novel type of classification for these polynomials is indicated. Next, infinite sequences of identities for various Bessel functions and for power functions are derived. New identities for trigonometric functions are also given, as well as brief miscellanea on: functions resembling Dirac's delta function, integral transforms and a functional equation.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 64 , Issue 1 , January 1968 , pp. 105 - 112
Copyright
Copyright © Cambridge Philosophical Society 1968

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

(1)Abdelkader, M. A.Problem 65–4. SIAM Rev. 7 (1965), 410;CrossRefGoogle Scholar
Abdelkader, M. A.Problem 65–4. SIAM Rev. 8 (1966), 526–529.CrossRefGoogle Scholar
(2)Carlitz, L.A binomial identity arising from a sorting problem. SIAM Rev. 6 (1964), 20–30.CrossRefGoogle Scholar
(3)Carlitz, L.Some multiple sums and binomial identities. J. Soc. Indust. Appl. Math. 13 (1965), 469–486.CrossRefGoogle Scholar
(4)Courant, R. and Hilbert, D.Methoden der Mathematischen Physik, I, p. 76 (Springer: Berlin, 1931).CrossRefGoogle Scholar
(5)Jahnke, E. and Emde, F.Tables of functions, p. 32 (Dover; New York, 1945).Google Scholar
(6)Watson, G. N.A treatise on the theory of Bessel functions, second ed. (Cambridge University Press, 1962).Google Scholar