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Parseval Relations for Kontorovich-Lebedev Transforms

Published online by Cambridge University Press:  20 January 2009

J. S. Lowndes
Affiliation:
Royal College of Advanced Technology, Salford 5, Lancashire
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The Kontorovich-Lebedev Transform of a function f(r), 0<r<∞, may be written in a general form as fg(μ) where,

Type
Research Article
Copyright
Copyright © Edinburgh Mathematical Society 1962

References

REFERENCES

(1) Snow, C., Hypergeometric and Legendre Functions etc., N.B.S. Appl. Maths. Series 19 (1952).Google Scholar
(2) Kontorovich, M. J. and Lebedev, N. N., J. Phys. U.S.S.R., 1 (1939), 229.Google Scholar
(3) Lebedev, N. N., (Doklady), Akad. Sci. U.S.S.R. (N.S.), 52 (1946), 655.Google Scholar
(4) Lebedev, N. N., (Doklady), Akad. Nauk. S.S.S.R. (N.S.), 58 (1947), 1007.Google Scholar
(5) Lebedev, N. N., (Doklady), Akad. Nauk. S.S.S.R., Prinkl. Mat. Meh. 13, (1949), 465.Google Scholar
(6) Turner, R. D., Quart. Appl. Math., 14 (1956), 63.Google Scholar
(7) Wells, C. P. and Leitner, A., Quart. Appl. Math., 15 (1958), 430.Google Scholar
(8) Lowndes, J. S., Proc. Edin. Math. Soc, 11, 3 (1959), 135.Google Scholar
(9) Erdelyi, et al. , Tables of Integral Transforms, Vol. 2 (McGraw-Hill, 1954).Google Scholar
(10) Lowndes, J. S., Siam Review (April, 1961)Google Scholar