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On formulas for π experimentally conjectured by Jauregui--Tsallis.

Amdeberhan, T. and Borwein, Jonathan M. and Straub, Armin (2012) On formulas for π experimentally conjectured by Jauregui--Tsallis. J. Math. Physics, 53 .

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    Abstract

    In a recent study of representing Dirac's delta distribution using q-exponentials, M. Jauregui and C. 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.

    Item Type: Article
    Additional Information: Galleys July 2012.
    Subjects: UNSPECIFIED
    Faculty: UNSPECIFIED
    Depositing User: Dr David Allingham
    Date Deposited: 05 Oct 2012 13:13
    Last Modified: 03 Jan 2015 14:23
    URI: https://docserver.carma.newcastle.edu.au/id/eprint/1378

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