On formulas for \(\pi\) experimentally conjectured by Jauregui-Tsallis (Q2865528)
From MaRDI portal
 | This is the item page for this Wikibase entity, intended for internal use and editing purposes. Please use this page instead for the normal view: On formulas for \(\pi\) experimentally conjectured by Jauregui-Tsallis |
scientific article; zbMATH DE number 6234871
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On formulas for \(\pi\) experimentally conjectured by Jauregui-Tsallis |
scientific article; zbMATH DE number 6234871 |
Statements
29 November 2013
0 references
hypergeometric function
0 references
Carlson's theorem
0 references
Chebyshev polynomial
0 references
orthogonal polynomials
0 references
Pfaff-Saalschütz identity
0 references
0 references
On formulas for \(\pi\) experimentally conjectured by Jauregui-Tsallis (English)
0 references
In exploring applications of the \(q\)-exponential function and formal representations of Dirac's delta distribution, Jauregui and Tsallis experimentally discovered formulae for \(\pi\) as hypergeometric series, as well as certain integrals.NEWLINENEWLINENEWLINENEWLINEIn this paper, rigorous proofs of these identities are offered using various methods. In offering several proofs of the Jauregui-Tsallis identities, the primary intent of this work is to lay down an illustration of the many technical underpinnings of such integral evaluations. In particular, an explicit discussion of creative telescoping and Carlson's Theorem is given.NEWLINENEWLINENEWLINENEWLINEMoreover, natural generalizations of the Jauregui-Tsallis identities to integrals involving Chebyshev polynomials are presented.
0 references
