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A confluent hypergeometric integral equation

Published online by Cambridge University Press:  18 May 2009

E. R. Love
Affiliation:
The University of Melbourne, Parkville 3052, Australia
T. R. Prabhakar
Affiliation:
The University of Delhi, Delhi 110007, India
N. K. Kashyap
Affiliation:
The University of Delhi, Delhi 110007, India
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Recently there have appeared papers ([7], [8]; also see [9]) in which integral equations with kernels involving the confluent hypergeometric function

have been studied. These equations are mainly Volterra equations of the first kind except that they have infinite domain (0, ∞). The rest are of the related type with integrals over (x, ∞) instead of (0, x); and all are convolution equations.

Type
Research Article
Copyright
Copyright © Glasgow Mathematical Journal Trust 1982

References

REFERENCES

1.Erdélyi, A., Magnus, W., Oberhettinger, F. and Tricomi, F. G.. Higher Transcendental Functions Vol. 1 (McGraw-Hill, 1953).Google Scholar
2.Lighthill, M. J., Fourier Analysis and Generalized Functions (Cambridge, 1958).Google Scholar
3.Love, E. R., Some integral equations involving hypergeometric functions, Proc. Edinburgh Math. Soc. (2) 15 (1967), 169198.Google Scholar
4.Love, E. R., Two more hypergeometric integral equations, Proc. Cambridge Phil. Soc. 63 (1967), 10551076.CrossRefGoogle Scholar
5.Love, E. R., A hypergeometric integral equation in Fractional Calculus and its Applications (edited by Ross, B.) (Springer Lecture Notes No 457, 1974) 272288.Google Scholar
6.Miller, K. S., The Weyl fractional calculus in Fractional Calculus and its Applications (edited by Ross, B.) (Springer Lecture Notes No 457, 1974) 8089.Google Scholar
7.Prabhakar, T. R., Two singular integral equations involving confluent hypergeometric functions, Proc. Cambridge Phil. Soc. 66 (1969), 7189.Google Scholar
8.Prabhakar, T. R., Some integral equations with Kummer's function in the kernels, Canad. Math. Bull. 14 (1971), 391404.Google Scholar
9.Srivastav, H. M. and Buschman, R. G., Convolution Integral Equations with Special Function Kernels (Wiley Eastern, Delhi, 1976).Google Scholar
10.Widder, D. V., The Laplace Transform (Princeton, 1946).Google Scholar