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On a generalized L–H transform

Published online by Cambridge University Press:  24 October 2008

V. K. Kapoor  and
S. Masood
V. K. Kapoor
Affiliation:
Banaras Hindu University, India
S. Masood
Affiliation:
Banaras Hindu University, India
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Abstract

The authors, while attempting to give a new generalization of the Laplace transform, have come across a particular function in the form of Meijer's G-function

which, when taken as a nucleus of the transformation K(x) in

defines a new transform. This transform besides serving as a generalization of the Laplace transform and most of its generalizations existing in the literature bears the characteristic property of generalizing the Hankel transform (and hence some of its generalizations) as well. In this paper the authors after having defined the transform have given an inversion theorem which is supported by means of two examples.

Information

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 64 , Issue 2 , April 1968 , pp. 399 - 406
Copyright
Copyright © Cambridge Philosophical Society 1968

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References

REFERENCES

(1)Bhise, V. M.Inversion formulae for a generalised Laplace integral. J. Vikram Univ. (1959), 57–63.Google Scholar
(2)Bhonsle, B. R.On integro-exponential function Ev(x). Bull. Calcutta Math. Soc. 49 (1957), 157–62.Google Scholar
(3)Bromwich, T. J. I'a.An introduction to the theory of infinite series. (London, 1931).Google Scholar
(4)Erdélyi, A.Higher transcendental functions, vol. I (New York, 1953).Google Scholar
(5)Erdélyi, A.Tables of integral transforms, vol. II (New York, 1954).Google Scholar
(6)Erdélyi, A.On a generalisation of Laplace transformation. Proc. Edinburgh Math. Soc. 2nd series, 10 (1954), 53–65.Google Scholar
(7)Kapoor, V. K.A generalisation of the Laplace transform (in the Press).Google Scholar
(8)Mainra, V. P.A new generalisation of the Laplace transform. Bull. Calcutta Math. Soc. 53 (1961), 23–31.Google Scholar
(9)Mehra, A. N. Thesis on ‘Meijer transform of one and two variables’ approved for Ph.D. degree by the Lucknow University in 1958.Google Scholar
(10)Meijer, C. S.Eine neue Erweiterung der Laplace transformation. Nederl. Akad. Wetensch. 44 (1941), 727–737.Google Scholar
(11)Roop, NarainOn a generalisation of Hankel transform and self-reciprocal functions. Univ. e Politec. Torino. Rend. Sem. Mat. 16 (1956–1957), 269–300.Google Scholar
(12)Roop, NarainA Fourier kernel. Math. Z. 70 (1959), 297–299.Google Scholar
(13)Titchmarsh, E. C.Introduction to the theory of Fourier integral (Oxford, 1948).Google Scholar
(14)Saxena, K. M.Inversion formulae for a generalised Laplace integral. Proc. Nat. Inst. Sci. (India) 19 (1953), 173–81.Google Scholar
(15)Saxena, R. K.Some theorems on generalised Laplace transform I. Proc. Nat. Inst. Sci. (India) 26 (1960), 400–13.Google Scholar
(16)Varma, R. S.On a generalisation of the Laplace integral. Proc. Nat. Acad. Sci. (India) 20 (1951), 209–16.Google Scholar
(17)Whittaker, E. T. and Watson, G. N.Modern analysis (Cambridge, 1927).Google Scholar