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A Relation between Laplace and Hankel Transforms

Published online by Cambridge University Press:  18 May 2009

B. R. Bhonsle
B. R. Bhonsle
Affiliation:
Government College of Engineering and Technology, Raipur (M.P.), India
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The Laplace transform of a function f(t) ∈ L(0, ∞) is defined by the equation

and its Hankel transform of order v is defined by the equation

The object of this note is to obtain a relation between the Laplace transform of tμf(t) and the Hankel transform of f(t), when ℛ(μ) > − 1. The result is stated in the form of a theorem which is then illustrated by an example.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 5 , Issue 3 , January 1962 , pp. 114 - 115
Copyright
Copyright © Glasgow Mathematical Journal Trust 1962

References

1.Sneddon, I. N., Fourier transforms (McGraw-Hill, New York, 1951).Google Scholar
2.Erdélyi, A., editor, Tables of integral transforms (McGraw-Hill, New York, 1954), vol. 1.Google Scholar