Applications of Laplace transforms and their inverses
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- by Charles Fox
- Proc. Amer. Math. Soc. 35 (1972), 193-200
- DOI: https://doi.org/10.1090/S0002-9939-1972-0300017-4
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Abstract:
By means of Laplace transforms and their inverses we first solve the Varma transform, considered as an integral equation for an unknown function in the integrand. We then express two operators of fractional integration in terms of Laplace and inverse Laplace transforms.References
- A. Erdélyi, On some functional transformations, Univ. e Politec. Torino Rend. Sem. Mat. 10 (1951), 217–234. MR 47818
- Charles Fox, Solving integral equations by $L$ and $L^{-1}$ operators, Proc. Amer. Math. Soc. 29 (1971), 299–306. MR 280944, DOI 10.1090/S0002-9939-1971-0280944-6
- H. Kober, On fractional integrals and derivatives, Quart. J. Math. Oxford Ser. 11 (1940), 193–211. MR 3269, DOI 10.1093/qmath/os-11.1.193
- R. K. Saxena, An inversion formula for the Varma transform, Proc. Cambridge Philos. Soc. 62 (1966), 467–471. MR 196426, DOI 10.1017/s030500410004007x A. Erdélyi et al. (Editors), Tables of integral transforms. Vol. 1, McGraw-Hill, New York, 1954. —, Tables of integral transforms. Vol. 2, McGraw-Hill, New York, 1954. E. C. Titchmarsh, Introduction to the theory of Fourier integrals, Clarendon Press, Oxford, 1937.
- R. S. Varma, On a generalization of Laplace integral, Proc. Nat. Acad. Sci. India Sect. A 20 (1951), 209–216. MR 61697
- G. N. Watson, A treatise on the theory of Bessel functions, Cambridge Mathematical Library, Cambridge University Press, Cambridge, 1995. Reprint of the second (1944) edition. MR 1349110
- E. T. Whittaker and G. N. Watson, A course of modern analysis, Cambridge Mathematical Library, Cambridge University Press, Cambridge, 1996. An introduction to the general theory of infinite processes and of analytic functions; with an account of the principal transcendental functions; Reprint of the fourth (1927) edition. MR 1424469, DOI 10.1017/CBO9780511608759
Bibliographic Information
- © Copyright 1972 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 35 (1972), 193-200
- MSC: Primary 44A10; Secondary 45H05
- DOI: https://doi.org/10.1090/S0002-9939-1972-0300017-4
- MathSciNet review: 0300017