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An Expansion of the Laguerre Polynomials, Lαn(z)

Published online by Cambridge University Press:  20 November 2018

Max Wyman
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Extract

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By a result due to Tricomi(1), it is known that the La guerre polynomials have an expansion in terms of the Bessel functions, Jv(z), of the form

1.1

where the coefficients Am are determined by

1.2

and

1.3

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 5 , Issue 3 , September 1962 , pp. 229 - 240
Copyright
Copyright © Canadian Mathematical Society 1962

References

1. Higher Transcendental Functions, Bateman Manuscript Project, McGraw Hill, 1953, Vol. 2, page 199.

2. Loc. Cit.

3. Asymptotic Solutions of Differential Equations with Transition Points or Singularities, Journal of Math. Physics, Vol. 1, No. 1 pp. 12-20, 1960.

4. This definition has not as yet been published.