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Annali di Matematica Pura ed Applicata

, Volume 65, Issue 1, pp 97–111 | Cite as

Bateman's expansion for the product of two Bessel functions

  • W. A. Al-Salam
  • L. Carlitz
Article
  • 159 Downloads

Summary

The general solution
$$g_v (z)\mathop \Sigma \limits_{n = 0}^\infty ( - 1)^n c_n^v z^n (c_0^v = 1)$$
of the functional equation
$$\begin{gathered} g_\mu ((1 - x)(1 - y)z)g_v (xyz) \hfill \\ = \mathop \Sigma \limits_{n = 0}^\infty ( - 1)^n \frac{{n!A_n (x)A_n (y)}}{{(\mu + 1)_n (v + 1)_n (\mu + n + 1)_n }}z^n g_\mu + v + 2n + 1(z) \hfill \\ \end{gathered} $$
, where An(x)=An(μ, υ) (x) is a polynomial in x of degree n, is obtained.

Keywords

General Solution Functional Equation Bessel Function 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. [1]
    G N. Watson,Theory of Bessel Functions, second edition, Cambridge, 1944.Google Scholar

Copyright information

© Nicola Zanichelli Editore 1964

Authors and Affiliations

  • W. A. Al-Salam
  • L. Carlitz

There are no affiliations available

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