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A procedure for deriving inversion formulae for integral transform pairs of a general kind

Published online by Cambridge University Press:  18 May 2009

Ian N. Sneddon
Ian N. Sneddon
Affiliation:
University of Glasgow
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In recent years there have appeared solutions of several integral equations of the type

in which the kernel K(x) contains (as a factor) one of the classical orthogonal polynomials or a hypergeometric function.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 9 , Issue 1 , January 1968 , pp. 67 - 77
Copyright
Copyright © Glasgow Mathematical Journal Trust 1968

References

REFERENCES

1.Li, Ta, A new class of integral transforms, Proc. Amer. Math. Soc. 11 (1960), 290–298.CrossRefGoogle Scholar
2.Buschman, R. G., An inversion integral for a Legendre transformation, Amer. Math. Monthly 69 (1962), 288–289.CrossRefGoogle Scholar
3.Higgins, T. P., An inversion integral for a Gegenbauer transformation, J. Soc. Indust. Appl. Math. 11 (1963), 886–893.CrossRefGoogle Scholar
4.Srivastava, K. N., Inversion integrals involving Jacobi's polynomials, Proc. Amer. Math. Soc. 15 (1964), 635–638.Google Scholar
5.Srivastava, K. N., On some integral equations involving Jacobi polynomials, Math. Japon. 9 (1964), 85–88.Google Scholar
6.Erdélyi, A., An integral equation involving Legendre functions, J. Soc. Indust. Appl. Math. 12 (1964), 15–30.CrossRefGoogle Scholar
7.Higgins, T. P., A hypergeometric function transform, J. Soc. Indust. Appl. Math. 12 (1964), 601–612.CrossRefGoogle Scholar
8.Wimp, Jet, Two integral transform pairs involving hypergeometric functions, Proc. Glasgow Math. Assoc. 7 (1965), 42–44.CrossRefGoogle Scholar
9.Sneddon, I. N., Fourier transforms, McGraw-Hill (New York, 1951).Google Scholar
10.Slater, L. J., Generalized hypergeometric functions, Cambridge University Press (Cambridge, 1966).Google Scholar
11.Erdélyi, A. et al. , Tables of integral transforms, Vol. 1, McGraw-Hill (New York, 1954).Google Scholar