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On Self-reciprocal functions for Fourier-Bessel integral transforms

Published online by Cambridge University Press:  24 October 2008

Afzal Ahmad  and
V. Lakshmikanth
Afzal Ahmad
Affiliation:
Osmania UniversityHyderabad (A.P.), India
V. Lakshmikanth
Affiliation:
Osmania UniversityHyderabad (A.P.), India
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Extract

Following Hardy and Titchmarsh(1) a function f(x) is said to be self-reciprocal if it satisfies the Fourier-Bessel integral transform

where Jp(x) is a Bessel function of order P ≥ –½. This integral is denoted by Rp. The special cases P ½ and P ½, we denote by Rs and Rc, respectively.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 57 , Issue 4 , October 1961 , pp. 778 - 781
Copyright
Copyright © Cambridge Philosophical Society 1961

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References

REFERENCES

(1)Hardy, G. H. and Titchmarsh, E. C., Self reciprocal functions. Quart. J. Math. (2), 1 (1930), 196–231.Google Scholar
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(4)Lakshmikanth, V., Some self-reciprocal functions and kernels. Proc. Camb. Phil. Soc. 57 (1961), 690–2.Google Scholar
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