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Inversion of a class of transforms with a difference kernel

Published online by Cambridge University Press:  24 October 2008

V. K. Varma
V. K. Varma
Affiliation:
Engineering College, Bilaspur (M.P.), India
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Extract

1. Recently Ta li(10) Buschman(2, 3), Erdelyi(4) and Shrivastava(8, 9) obtained solutions of integral equations involving polynomial kernels in the range of integration x to 1. Widder(12) obtained an inversion of a convolution transform with a Laguerre polynomial as kernel.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 65 , Issue 3 , May 1969 , pp. 673 - 677
Copyright
Copyright © Cambridge Philosophical Society 1969

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References

REFERENCES

(1)Bateman, H.Partial differential equations of mathematical physics (Cambridge, 1932).Google Scholar
(2)Buschman, R. G.An inversion integral for a Legendre transformation. Amer. Math. Monthly 69 (1962), 288–289.CrossRefGoogle Scholar
(3)Buschman, R. G.An inversion integral. Proc. Amer. Math. Soc. 13 (1962), 675–677.CrossRefGoogle Scholar
(4)Erdélyi, A.An integral equation involving Legendre's polynomial. Amer. Math. Monthly 70 (1963), 651–652.CrossRefGoogle Scholar
(5)Erdélyi, A.Tables of integral transforms, vol. 2 (McGraw Hill; New York, 1954).Google Scholar
(6)Erdélyi, A.Higher transcendental functions, vol. 1 (McGraw Hill; New York, 1953).Google Scholar
(7)Hopf, E.Mathematical problems of radiative equilibrium. Cambridge Tracts no. 31 (1933).Google Scholar
(8)Shrivastava, K. N.A class of integral equations involving ultraspherical polynomials as kernel. Proc. Amer. Math. Soc. 14 (1963), 932–940.CrossRefGoogle Scholar
(9)Shrivastava, K. N.Inversion integrals involving Jacobi's polynomials. Proc. Amer. Math. Soc. 15 (1964), 635–638.Google Scholar
(10)Ta, li. A new class of integral transforms. Proc. Amer. Math. Soc. 11 (1956), 290–298.Google Scholar
(11)Titchmarsh, E. C.Theory of Fourier integrals (Oxford, 1948).Google Scholar
(12)Widder, D. V.The convolution transform whose kernel is a Laguerre polynomial. Amer. Math. Monthly 70 (1963), 291–93.CrossRefGoogle Scholar