Related papers: On simplifications of certain $q$-multisums

Recursive formulas extending some known $_{2}F_{1}$ and $_{3}F_{2}$ summation formulas by using contiguous relations have been obtained. On the one hand, these recursive equations are quite suitable for symbolic and numerical evaluation by…

A large class of Feynman integrals, like e.g., two-point parameter integrals with at most one mass and containing local operator insertions, can be transformed to multi-sums over hypergeometric expressions. In this survey article we present…

With the help of a summation of basic hypergeometric series, the creative microscoping method recently introduced by Guo and Zudilin, and the Chinese remainder theorem for coprime polynomials, we find some new $q$-supercongruences.…

In the present paper, we establish a general transformation for $q$-series which contains L. Wang et al's transformation involved in Nahm series. As direct applications, some concrete new transformation formulas for the ${}_{r+1}\phi_r$…

The review of modern study of algebraic, geometric and differential properties of quaternionic (Q) numbers with their applications. Traditional and "tensor" formulation of Q-units with their possible representations are discussed and groups…

For the quantum integer [n]_q = 1+q+q^2+... + q^{n-1} there is a natural polynomial multiplication such that [mn]_q = [m]_q \otimes_q [n]_q. This multiplication is given by the functional equation f_{mn}(q) = f_m(q) f_n(q^m), defined on a…

We give a method to embed the q-series in a (p,q)-series and derive the corresponding (p,q)-extensions of the known q-identities. The (p,q)-hypergeometric series, or twin-basic hypergeometric series (diferent from the usual bibasic…

We review recent results concerning the representation of conformal field theory characters in terms of fermionic quasi-particle excitations, and describe in detail their construction in the case of the integrable three-state Potts chain.…

From two q-summation formulas we deduce certain series expansion formulas involving the q-gamma function. With these formulas we can give q-analogues of series expansions for certain constants.

Using matrix inversion and determinant evaluation techniques we prove several summation and transformation formulas for terminating, balanced, very-well-poised, elliptic hypergeometric series.

The article addresses the problem whether indefinite double sums involving a generic sequence can be simplified in terms of indefinite single sums. Depending on the structure of the double sum, the proposed summation machinery may provide…

A systematic procedure for generating certain identities involving elementary symmetric functions is proposed. These identities, as particular cases, lead to new identities for binomial and q-binomial coefficients.

There are many similarities between the theories of matroids and $q$-matroids. However, when dealing with the direct sum of $q$-matroids many differences arise. Most notably, it has recently been shown that the direct sum of representable…

By applying the partial derivative operator to several summation formulas for hypergeometric series, we prove several double series for $\pi$ in this paper. Similarly, we also establish several $q$-analogues of them.

Some multiple hypergeometric transformation formulas arising from the balanced du- ality transformation formula are discussed through the symmetry. Derivations of some transformation formulas with different dimensions are given by taking…

Some new representations of the supersymmetric transformations are derived, and the supermultiplets are introduced. Based on these representations, various formulations (equations, commutation relations, propagators, Jacobi identities,…

A multi-parafermion basis of states for the Z_k parafermionic models is derived. Its generating function is constructed by elementary steps. It corresponds to the Andrews multiple-sum which enumerates partitions whose parts separated by the…

Multiple binomial sums form a large class of multi-indexed sequences, closed under partial summation, which contains most of the sequences obtained by multiple summation of products of binomial coefficients and also all the sequences with…

We examine the convergence of $q$-hypergeometric series when $|q|=1$.

In this paper, we will obtain a variety of interesting $q$-series containing central $q$-binomial coefficients. Our approach is based on manipulating deformed basic hypergeometric series.