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: |
Wiley
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 |
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| _version_ | 1849468903317569536 |
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| author | M. Aslam Chaudhry |
| author_facet | M. Aslam Chaudhry |
| author_sort | M. Aslam Chaudhry |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-ff6a1000cc974d60a3bfad3b1a4886ca |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2000-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-ff6a1000cc974d60a3bfad3b1a4886ca2025-08-20T03:25:42ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252000-01-012329910210.1155/S0161171200001150Laplace transform of certain functions with applicationsM. Aslam Chaudhry0Department of Mathematical Sciences, King Fahd University of Petroleum and Minerals, Dhahran, Saudi ArabiaThe 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.http://dx.doi.org/10.1155/S0161171200001150Laplace transformsprobability density functionsWhittaker functions. |
| spellingShingle | M. Aslam Chaudhry Laplace transform of certain functions with applications International Journal of Mathematics and Mathematical Sciences Laplace transforms probability density functions Whittaker functions. |
| title | Laplace transform of certain functions with applications |
| title_full | Laplace transform of certain functions with applications |
| title_fullStr | Laplace transform of certain functions with applications |
| title_full_unstemmed | Laplace transform of certain functions with applications |
| title_short | Laplace transform of certain functions with applications |
| title_sort | laplace transform of certain functions with applications |
| topic | Laplace transforms probability density functions Whittaker functions. |
| url | http://dx.doi.org/10.1155/S0161171200001150 |
| work_keys_str_mv | AT maslamchaudhry laplacetransformofcertainfunctionswithapplications |