On formulas for π experimentally conjectured by Jauregui–Tsallis

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
Language: eng
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