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Some Integral Equations with Rummer's Functions in the Kernels

  • Tilak Raj Prabhakar (a1)

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Since 1963 several authors ([13], [2], [6], [14], [10], [11], [12], [9]) have considered integral equations each one of which is contained as a special case in one of the two equations

1.1

1.2

for Re b > 0 and x ∊ [α, β].

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References

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1. Acźel, J., Lectures on functional equations and their applications, Academic Press, New York (1966), p. 38.
2. Buschman, R. G., Convolution equations with generalized Laguerre polynomial kernels, SI AM Rev. 6 (1964), 166-167.
3. Erdélyi, A., Some integral equations involving finite parts of divergent integrals, Glasgow Math. J. 8 (1967), 50-54.
4. Erdélyi, A., et. al., Higher transcendental functions, Vol. I, McGraw-Hill, New York, 1953.
5. Gelfand, I. M. and Shilov, G. E., Generalized functions, (translated from Russian), Vol. 1, Academic Press, New York, 1964.
6. Khandekar, P. R., On a convolution transform involving generalized Laguerre polynomial as its kernel, J. Math. Pures Appl. (9) 44 (1965), 195-197.
7. Love, E. R., Two more hypergeometric integral equations, Proc. Cambridge Philos. Soc. 63 (1967), 1055-1076.
8. Mikhlin, S. G., Linear Integral equations (translated from Russian), Hindustan, Delhi, (1960), p. 29.
9. Prabhakar, Tilak Raj, Two singular integral equations involving confluent hypergeometric functions, Proc. Cambridge Philos. Soc. 66 (1969), 71-89.
10. Rusia, K. C., An Integral Equation Involving Generalized Laguerre Polynomial, Math. Japon. 11 (1966), 15-18.
11. Srivastava, K. N., A class of integral equations involving Laguerre polynomials as kernel, Proc. Edinburgh Math. Soc. 15 (1966), 33-36.
12. Srivastava, K. N., On integral equations involving Whittaker's function, Proc. Glasgow Math. Assoc. 7 (1966), 125-127.
13. Widder, D. V., The inversion of a convolution transform whose kernel is a Laguerre polynomial, Amer. Math. Monthly 70 (1963), 291-293.
14.Jet Wimp, Two integral transform pairs involving hypergeometric functions, Proc. Glasgow Math. Assoc. 7 (1965), 42-44.
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