Hostname: page-component-7b7567c8c-wxvwp Total loading time: 0 Render date: 2026-11-15T18:30:55.391Z Has data issue: false hasContentIssue false
  • English
  • Français

Some Integral Equations with Rummer's Functions in the Kernels

Published online by Cambridge University Press:  20 November 2018

Tilak Raj Prabhakar
Tilak Raj Prabhakar*
Affiliation:
Ramjas College, University of Delhi, Delhi-7, India
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the 'Save PDF' action button.

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].

Information

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 14 , Issue 3 , September 1971, pp. 391 - 404
Copyright
Copyright © Canadian Mathematical Society 1971

References

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