On formulas for experimentally conjectured by

In a recent study of representing Dirac’s delta distribution usingq-exponentials, M. Jauregui and C. Tsallis experimentally discovered formulae for as hypergeometric series as well as certain integrals. Herein, we oer 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.