Related papers: The q-WZ Method for Infinite Series
In this paper we present a new identity and some of its variants which can be used for finding solutions while solving fractional infinite and finite series. We introduce another simple identity which is capable of generating solutions for…
We present alternative, q-hypergeometric proofs of some polynomial analogues of classical q-series identities recently discovered by Alladi and Berkovich, and Berkovich and Garvan.
For 1<p<infty, and weight w in A_p, and function f in L^p(w), we show that the r-variation of the Walsh-Fourier sums are finite, for r sufficiently large as function of w. (That r is a function of w is necessary.) This strengthens a result…
In this paper we derive two expressions for the Hurwitz zeta function involving the complete Bell polynomials in the restricted case where q is a positive integer greater than 1. The arguments of the complete Bell polynomials comprise the…
The Andrews-Bressoud identities are one of many families of $q$-series identities relating an infinite sum to an infinite product. While the original motivation for studying these series relates to partitions, they can also be viewed in…
We show that several terminating summation and transformation formulas for basic hypergeometric series can be proved in a straightforward way. Along the same line, new finite forms of Jacobi's triple product identity and Watson's quintuple…
We prove a new four parameter q-hypergeometric series identity from which the three parameter key identity for the Goellnitz theorem due to Alladi, Andrews, and Gordon, follows as a special case by setting one of the parameters equal to 0.…
In a recent article, Apagodu and Zeilberger (http://arxiv.org/abs/1606.03351)discuss some applications of an algorithm for finding and proving congruence identities (modulo primes) of indefinite sums of many combinatorial sequence. At the…
Recently Corteel and Welsh outlined a technique for finding new sum-product identities by using functional relations between generating functions for cylindric partitions and a theorem of Borodin. Here, we extend this framework to include…
The Cauchy identities play an important role in the theory of symmetric functions. It is known that Cauchy sums for the $q$-Whittaker and the skew Schur polynomials produce the same factorized expressions modulo a $q$-Pochhammer symbol. We…
Li-Zinger's hyperplane theorem states that the genus one GW-invariants of the quintic threefold is the sum of its reduced genus one GW-invariants and 1/12 multiplies of its genus zero GW-invariants. We apply the Guffin-Sharpe-Witten's…
This paper gives a new application of so-called connected sums, introduced recently by Seki and Yamamoto. Special about our approach is that it proves a duality for the Schlesinger-Zudilin and the Bradley-Zhao model of qMZVs simultaneously.…
It is shown that the classical quadratic and cubic transformation identities satisfied by the hypergeometric function ${}_3F_2$ can be extended to include additional parameter pairs, which differ by integers. In the extended identities,…
We establish two identities for Lambert series and double Lambert series, thereby resolving conjectures of Andrews, Dixit, Schultz and Yee (Acta Arith.~181:253--286, 2017), as well as Amdeberhan, Andrews and Ballantine (J Combin Theory…
We establish a $q$-analogue of Sun--Zhao's congruence on harmonic sums. Based on this $q$-congruence and a $q$-series identity, we prove a congruence conjecture on sums of central $q$-binomial coefficients, which was recently proposed by…
$q$-Supercongruences modulo the fifth and sixth powers of a cyclotomic polynomial are very rare in the literature. In this paper, we establish some $q$-supercongruences modulo the fifth and sixth powers of a cyclotomic polynomial in terms…
By solving an infinite nonlinear system of $q$-difference equations one constructs a chain of $q$-difference operators. The eigenproblems for the chain are solved and some applications, including the one related to $q$-Hahn orthogonal…
With the exception of q-hypergeometric summation, the use of computer algebra packages implementing Zeilberger's "holonomic systems approach" in a broader mathematical sense is less common in the field of q-series and basic hypergeometric…
We utilize the Wilf-Zeilberger (WZ) method to establish congruences related to truncated Ramanujan-type series. By constructing hypergeometric terms $f(k, a, b, \ldots)$ with Gosper-summable differences and selecting appropriate parameters,…
The well-known Kummer's formula evaluates the hypergeometric series 2F1(A,B;C;-1) when the relation B-A+C=1 holds. This paper deals with evaluation of 2F1(-1) series in the case when C-A+B is an integer. Such a series is expressed as a sum…