Hostname: page-component-77c89778f8-sh8wx Total loading time: 0 Render date: 2024-07-22T22:37:57.700Z Has data issue: false hasContentIssue false

On a Theorem in the Generalised Fourier Transform

Published online by Cambridge University Press:  20 November 2018

S. C. Mitra*
Affiliation:
University of Alberta
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.

The function was defined by G.N. Watson, [9, (i)]in 1931 by the integral relation

+ another term with μ and v interchanged;

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 1967

References

1. Bhatnagar, K. P., (i) On certain theorems on self-reciprocal functions, Acad. Roy. Belgique. Bull. cl. Sci. (5) 39, (1955), 42-69. (ii) Two theorems on self-reciprocal functions and a new transform. Bull. Calcutta Math. Soc. 45, (1955), 109-112.Google Scholar
2. Fox, Charles, (i) The Gand H Functions as symmetrical Fourier Kernels, Trans. American Math. Soc. (1966) 98, 395-429.Google Scholar
3. Mainra, V. P., (i) On Poisson's formulae. Bull. Cal. Math. Soc. 49 (1955), 163-176. (ii) A new transform, Bull. Cal. Math. Soc. 1955 Supplement 76-93.Google Scholar
4. Meijer, C. S., (i) On the G. Function. Proc. Neder. Akad. Wetensch. (1944), 49, 227-237, 344-356, 457-469, 632-641, 765-772, 936-943, 1062-1072, 1165-1175.Google Scholar
5. Singh, B., (i) On certain expansions and integrals involving . Proc. Rajasthan Acad. Sci. 9(1966)9-22.Google Scholar
6. Singh, P., (i) Thesis for the Ph. D. degree. B.I.T.S. (Pilani) To appear in the Proc. Nat. Acad, of Science. Allahalad (1966).Google Scholar
7. Singh, Y. P., (i) Thesis for the Ph. D. degree B.I.T.S. (Pilani) India (1960). See (Scientific Journal, Benaras Univ. 1966).Google Scholar
8. Titchmarsh, E. C., (i) Theory of Fourier Integrals, 1966 (Oxford).Google Scholar
9. Watson, G. N., (i) Some self - reciprocal functions. Quart. J. Math., ‘ (Oxford) 2, (1933)298-309. (ii) A treatise on the Theory of Bessel Functions, Camb. Univ. Press (1966).Google Scholar