Laplace transform of certain functions with applications
The Laplace transform of the functions tν(1+t)β, Reν>−1, is expressed in terms of Whittaker functions. This expression is exploited to evaluate infinite integrals involving products of Bessel functions, powers, exponentials, and Whittaker functions. Some special cases of the result are discussed....
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| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
2000-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S0161171200001150 |
| Summary: | The Laplace transform of the functions tν(1+t)β, Reν>−1, is expressed in terms of Whittaker functions. This
expression is exploited to evaluate infinite integrals involving
products of Bessel functions, powers, exponentials, and
Whittaker functions. Some special cases of the result
are discussed. It is also demonstrated that the famous identity∫0∞sin (ax)/x dx=π/2 is a special case of our
main result. |
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| ISSN: | 0161-1712 1687-0425 |