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Some self-reciprocal functions and kernels

Published online by Cambridge University Press:  24 October 2008

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

The aim of this note is to find out some self-reciprocal functions and kernels for Fourier-Bessel integral transforms. Following Hardy and Titchmarsh(i), we shall denote by Rp the class of functions which satisfy the homogeneous integral equation

where Jp(x) is a Bessel function of order p ≥ − ½. For particular values of p = ½, − ½, we write Rs and Rc irrespectively.

Type
Research Notes
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 57 , Issue 3 , July 1961 , pp. 690 - 692
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.CrossRefGoogle Scholar
(2)Lakshmikanth, V.Some self-reciprocal functions. Proc. Nat. Acad. Sci. India, Part A, 28 (1959), 246–8.Google Scholar
(3)Lakshmikanth, V. On the relation between the self-reciprocal functions and kernels (submitted for publication).Google Scholar
(4)Rao, M. E. NarayanSome general kernels for the derivation of self reciprocal functions. Proc. Indian Acad. Sci. Sect. A, 50 (1959), 385–91.CrossRefGoogle Scholar
(5)Gupta, H. C.TWO theorems on self-reciprocal functions. J. Indian Math. Soc. N.S. 9 (1945), 66–8.Google Scholar
(6)Watson, G. N.Theory of Bessel functions (Cambridge, 1922).Google Scholar