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Some triple series equations involving Jacobi polynomials

Published online by Cambridge University Press:  20 January 2009

J. S. Lowndes
J. S. Lowndes
Affiliation:
University of StrathclydeGlasgow
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Equations which may be regarded as extensions of the dual series equations discussed by Noble (1) and the present author (2) are the triple series equations of the first kind

and the triple series equations of the second kind

where f, f1, g, g1h and h1 are all known functions,

is the Jacobi polynomial (3).

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 16 , Issue 2 , December 1968 , pp. 101 - 108
Copyright
Copyright © Edinburgh Mathematical Society 1968

References

REFERENCES

(1) Noble, B., Some dual series equations involving Jacobi polynomials, Proc. Camb. Phil. Soc. 59 (1963), 363.Google Scholar
(2) Lowndes, J. S., Dual series and triple integral equations, (to be published).Google Scholar
(3) Magnus, W. and Oberhettinger, F., Formulas and theorems for the functions of mathematical physics (Chelsea, 1954).Google Scholar
(4) Erdelyi, A. et al. , Higher transcendental functions (McGraw-Hill, 1953).Google Scholar
(5) Srivastava, K. N., On triple series equations involving series of Jacobi polynomials, Proc. Edin. Math. Soc. 15 (1967), 221.Google Scholar
(6) Collins, W. D., On some triple series equations and their applications, Arch. Rat. Mech. Anal. 11 (1962) 122.Google Scholar
(7) Cooke, J. C., Triple integral equations, Quart. Journ. Mech. Appl. Math. 16 (1963), 193.Google Scholar