A Method for Evaluating Definite Integrals in terms of Special Functions with Examples
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2019
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| _version_ | 1866929658129285120 |
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| author | Reynolds, Robert Stauffer, Allan |
| author_facet | Reynolds, Robert Stauffer, Allan |
| contents | We present a method using contour integration to derive definite integrals and their associated infinite sums which can be expressed as a special function. We give a proof of the basic equation and some examples of the method. The advantage of using special functions is their analytic continuation which widens the range of the parameters of the definite integral over which the formula is valid. We give as examples definite integrals of logarithmic functions times a trigonometric function. In various cases these generalizations evaluate to known mathematical constants such as Catalan's constant and $π$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1906_04927 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | A Method for Evaluating Definite Integrals in terms of Special Functions with Examples Reynolds, Robert Stauffer, Allan Number Theory 30E20, 33-01, 33-03, 33-04, 33-33B We present a method using contour integration to derive definite integrals and their associated infinite sums which can be expressed as a special function. We give a proof of the basic equation and some examples of the method. The advantage of using special functions is their analytic continuation which widens the range of the parameters of the definite integral over which the formula is valid. We give as examples definite integrals of logarithmic functions times a trigonometric function. In various cases these generalizations evaluate to known mathematical constants such as Catalan's constant and $π$. |
| title | A Method for Evaluating Definite Integrals in terms of Special Functions with Examples |
| topic | Number Theory 30E20, 33-01, 33-03, 33-04, 33-33B |
| url | https://arxiv.org/abs/1906.04927 |