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A note on the associated Legendre polynomials

Published online by Cambridge University Press:  18 May 2009

P. R. Khandekar
P. R. Khandekar
Affiliation:
Motilal Vlgyan MahavidyalayaBhopal (M.P.)India
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Extract

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This paper is paper gives what appears to be a new Rodrigues’ formula for the Associated Legendre Polynomials defined by [5, p. 122]

with the restriction that m is an even positive integer, which helps to evaluate some integrals. Putting m = 2k in (1.1) and replacing Pn(x) by the Gegenbauer Polynomial and using [3, p. 176]

We obtain

Putting a =v–½ in the relation [4, p. 283]

We get

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 6 , Issue 3 , January 1964 , pp. 156 - 160
Copyright
Copyright © Glasgow Mathematical Journal Trust 1964

References

REFERENCES

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3.Erdélyi, A. et al. , Higher transcendental functions, Vol. II (New York, 1953).Google Scholar
4.Erdélyi, A. et al. , Tables of integral transforms, Vol. II (New York, 1954).Google Scholar
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