- Title
- On formulas for π experimentally conjectured by Jauregui–Tsallis
- Creator
- Amdeberhan, Tewodros; Borwein, David; Borwein, Jonathan M.; Straub, Armin
- Relation
- Journal of Mathematical Physics Vol. 53, Issue 7
- Publisher Link
- http://dx.doi.org/10.1063/1.4735283
- Publisher
- American Institute of Physics (AIP)
- Resource Type
- journal article
- Date
- 2012
- Description
- In a recent study of representing Dirac's delta distribution using q-exponentials, Jauregui and Tsallis experimentally discovered formulae for π as hypergeometric series as well as certain integrals. Herein, we offer rigorous proofs of these identities using various methods and our primary intent is to lay down an illustration of the many technical underpinnings of such evaluations. This includes an explicit discussion of creative telescoping and Carlson's Theorem. We also generalize the Jauregui–Tsallis identities to integrals involving Chebyshev polynomials. In our pursuit, we provide an interesting tour through various topics from classical analysis to the theory of special functions.
- Subject
- exponential distribution; geometry; integral equations; polynomials
- Identifier
- http://hdl.handle.net/1959.13/940209
- Identifier
- uon:12972
- Identifier
- ISSN:0022-2488
- Rights
- © 2012 American Institute of Physics
- Language
- eng
- Full Text
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