Hostname: page-component-586b7cd67f-g8jcs Total loading time: 0 Render date: 2024-11-26T07:25:50.141Z Has data issue: false hasContentIssue false
  • English
  • Français

Self reciprocal properties of certain functions

Published online by Cambridge University Press:  24 October 2008

V. V. L. N. Rao
V. V. L. N. Rao
Affiliation:
MusheerabadHyderabad (Dn)-20, India
Get access Rights & Permissions [Opens in a new window]

Extract

The object of this note is to study the properties of some functions self reciprocal in the Hankel transform. I denote a function f(x) as Rμ, if it is self reciprocal for Hankel transforms of order μ so that it is given by

where Jμ(x) is a Bessel function of order μ. If μ = ½, f(x) is denoted by Rs while f(x) is written as Rc when μ = − ½.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 57 , Issue 3 , July 1961 , pp. 561 - 567
Copyright
Copyright © Cambridge Philosophical Society 1961

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

(1)Brij, Mohan. A class of kernels. J. Banaras Hindu University. Silver Jubilee number (1942), pp. 134–7.Google Scholar
(2)Brij, Mohan. Formula connecting self reciprocal functions. Indian J. Phys. 15 (1951), 337–41.Google Scholar
(3)Brij, Mohan. A short note on self reciprocal functions. Bull. Calcutta Math. Soc. 31 (1939), 17.Google Scholar
(4)Brij, Mohan.Some infinite integrals. J. Indian Math. Soc. (N.S.), 5 (1941), 127.Google Scholar
(5)Dines-Chandra, . On Hankel transform of generalized hypergeometric functions. J. Indian Math. Soc. (N.S.), 16 (1952), 41–5.Google Scholar
(6)Hari, Shanker.On the Hankel transform of generalized hypergeometric functions. J. Lond. Math. Soc. 21 (1946), 198.Google Scholar
(7)Hardy, G. H.On Mellin's inversion formula. Messeng. Math. 47 (1918), 178–84.Google Scholar
(8)Meijer, C. S.Integral-darstellungen der Besselchen functionen. K. Nederlandse Akad. Wetensch. Proc. Ser. A, 37 (1934), 806.Google Scholar
(9)MacRobert, T. M.Derivation of Legendre function formulae from Bessel function formulae. Phil. Mag. (7), 21 (1936), 697.CrossRefGoogle Scholar
(10)MacRobert, T. M.Integrals of Legendre and Bessel functions. Quart. J. Math. (2), 11 (1940), 99.Google Scholar
(11)Sneddon, I. N.Special junctions of mathematical physics and chemistry (London, 1956).Google Scholar
(12)Varma, R. S.Some infinite integrals involving Weber's parabolic cylinder functions. J. Indian Math. Soc. (N.S.), 3 (1938), 25.Google Scholar
(13)Rao, V. V. L. N.Some self reciprocal functions and kernels. Proc. Camb. Phil. Soc. 55, (1959), 62–5.CrossRefGoogle Scholar
(14)Rao, V. V. L. N. Functions self reciprocal in Hankel transform (in the Press).Google Scholar