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A Class of Integral Equations Involving Laguerre Polynomials as Kernel

Published online by Cambridge University Press:  20 January 2009

K. N. Srivastava
K. N. Srivastava
Affiliation:
M.A. College of Technology, Bhopal (M.P.), India
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Recently Widder (3) has obtained inversion integrals for a convolution transform whose kernel is a Laguerre polynomial. Buschman (1) has considered convolution equations withgeneralised Laguerre polynomial kernel. His result includes that of Widder. However no attempt has so far been made towards the study of singular integral equations involving Laguerre polynomials as kernel. Here the author obtains an inversion integral for such an equation.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 15 , Issue 1 , June 1966 , pp. 33 - 36
Copyright
Copyright © Edinburgh Mathematical Society 1966

References

REFERENCES

(1)Buschman, R. G.Convolution equations with generalised Laguerre poly-nomial kernels, Notices Amer. Math. Soc, 10 (4) (1963), 374.Google Scholar
(2)Erdelyi, A.Higher Transcendental Functions, Vol. 2 (McGraw-Hill, New York, 1953).Google Scholar
(3)Widder, D. V.The inversion of a convolution transform whose kernel is a Laguerre polynomial, Amer. Math. Monthly, 70 (1963), 291–293.CrossRefGoogle Scholar