View Proposal #403
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| ID | 403 |
|---|---|
| First Name | Brian |
| Last Name | Diaz |
| Institution | Cornell College |
| Speaker Category | undergraduate student |
| Title of Talk | An Elementary Solution to a Problem of Ramanujan's Interest |
| Abstract | In the early 1900's, Srinivasa Ramanujan discovered an intriguing, yet exotic, integral that he believed could have a 'simple', beautiful closed form. However, he never gave a simple solution to this integral. It wouldn't be until the mid-1950's when Russian mathematician V. I. Levin revisited Ramanujan's integral. He used non-elementary calculus techniques to prove that the integral, indeed, had a closed form for a single parameter; however, that parameter was only defined for positive integers. The integral would not be fully explored for the sake of itself until half a century later. Recently, V. Adamchik found that exact same integral that Ramanujan had encountered nearly a century ago. He showed a closed form using methods of Euler sums and related non-elementary techniques. This presentation will show a closed form of the integral does exist, but use only methods of elementary calculus. In addition, these techniques can be used to extend the result to double parameters! |
| Subject area(s) | |
| Suitable for undergraduates? | Y |
| Day Preference | Either |
| Computer Needed? | N |
| Bringing a laptop? | N |
| Overhead Needed? | |
| Software requests | |
| Special Needs | |
| Date Submitted | 10/07/2014 |
| Year | 2014 |