scientific article; zbMATH DE number 806502
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zbMath0847.33004MaRDI QIDQ4851969
Publication date: 21 November 1995
Full work available at URL: http://www.numdam.org/item?id=CM_1995__95_1_43_0
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Combinatorial identities, bijective combinatorics (05A19) Generalized hypergeometric series, ({}_pF_q) (33C20)
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Hidden \(q\)-analogues of Ramanujan-like \(\pi\)-series, Multifold inverse series relations and multivariate derivative identities, Quartic theta hypergeometric series, \( \pi \)-formulas from dual series of the Dougall theorem, Abel's method on summation by parts and theta hypergeometric series, Abel's lemma on summation by parts and basic hypergeometric series, Positivity preserving transformations for 𝑞-binomial coefficients, Duplicate form of Carlitz inversions and summation formulae, $q$-analogues of several $\pi $-formulas, Abel's lemma on summation by parts and terminating \(q\)-series identities, Ramanujan-like formulae for \(\pi\) and \(1/\pi\) via Gould-Hsu inverse series relations, Abel's method on summation by parts and nonterminating \(q\)-series identifies, Terminating balanced \({}_4\phi_3\)-series and very well-poised \({}_8\phi_7\)-series, Abel's Lemma on summation by parts and partial \(q\)-series transformations, A new multidimensional matrix inverse with applications to multiple \(q\)-series, Summation and transformation formulas for elliptic hypergeometric series.
Cites Work
- The method of creative telescoping
- Some inverse relations
- Sone new inverse series relations
- An Indefinite Bibasic Summation Formula and Some Quadratic, Cubic and Quartic Summation and Transformation Formulas
- Applications of q-Lagrange Inversion to Basic Hypergeometric Series
- Summation, Transformation, and Expansion Formulas for Bibasic Series
- On the q-Analogues of Some Transformations of Nearly-Poised Hypergeometric Series
- Strange Evaluations of Hypergeometric Series
- A new matrix inverse
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