Wenchang Chu

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Steven J. Miller

Williams College

Marta Diaz-Guardamino

Durham University

Arturo Erdely

Universidad Nacional Autónoma de México

John Uebersax

California Polytechnic State University at San Luis Obispo

Michael Neale

Virginia Commonwealth University

Viacheslav Kuleshov

Stockholm University

José Francisco Pessanha

UERJ - Universidade do Estado do Rio de Janeiro / Rio de Janeiro State University

Adebayo D Agunbiade

Olabisi Onabanjo University, Ago-Iwoye, Nigeria

Jorge Porras

Sonoma State University

Víctor Manuel García-Guerrero

El Colegio de México

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Papers by Wenchang Chu

Integrals of hyperbolic tangent function

Discrete mathematics letters, Apr 6, 2024

By means of the contour integration method, we evaluate, in closed form, a class of definite inte... more

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TERMINATING ALMOST POISED q-DIXON SUMS

Kyushu Journal of Mathematics

By means of the linearization method and the Carlitz-Sears transformation, the terminating almost... more

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Infinite Series Concerning Tails of Riemann Zeta Values

Axioms, Aug 2, 2023

Infinite series involving Riemann's zeta and Dirichlet's lambda tails, and weighted by three harm... more Infinite series involving Riemann's zeta and Dirichlet's lambda tails, and weighted by three harmonic-like elementary symmetric functions are examined. By means of integral representations of zeta tails together with the telescopic approach, twelve general summation theorems are established that express these series as coefficients of the bivariate beta function Beta(u, v). By further expanding Beta(u, v) into Laurent series in u and v, several explicit summation formulae are shown as consequences.

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Basic Hypergeometric Series

Quaderni di Matematica, 2004

Partitions and representations 1 A2. Ferrers diagrams of partitions 2 A3. Addition on partitions ... more Partitions and representations 1 A2. Ferrers diagrams of partitions 2 A3. Addition on partitions 6 A4. Multiplication on partitions 6 A5. Dominance partial ordering 7 Chapter B. Generating Functions of Partitions Il BI. Basic generating functions of partitions B2. Classical partitions and the Gauss formula B3. Partitions into distinct parts and the Euler formula 19 B4. Partitions and the Gauss q-binomial coefficients B5. Partitions into distinct parts and finite q-differences Chapter C . Durfee Rectangles and Classical Partition Identities Cl. q-Series identities of Cauchy and Kummer: Unification C2. q-Binomial convolutions and the Jacobi triple product C3. The finite form of Euler's pentagon number theorem Chapter D. The Carlitz Inversions and Rogers-Ramanujan Identities DI. Combinatorial inversions and series transformations D2. Finite q-differences and further transformation D3. Rogers-Ramanujan identities and their finite forms Chapter E. Basic Hypergeometric Series El. Introduction and notation E2. The q-Gauss summation formula E3. Transformations of Heine and Jackson E4. The q-Pfaff-Saalschiitz summation theorem E5 . The terminating q-Dougall-Dixon formula E6. The Sears balanced transformations E7. Watson's q-Whipple transformation vii viii CHU Wenchang and DI CLAUDIO Leontina Chapter F. Bilateral Basic Hypergeornetric Series Fl. Definition and notation F2. Rarnanuj an's bilateral -series identity F3. Bailey's bilateral identity F4. Bilateral q-analogue of Dixon's theorern F5. Partial fraction decornposition rnethod Chapter G. The Lagrange Four Square Theorern G 1. Representations by two square surns G2. Representations by four square surns G3. Representations by six square surns G4. Representations by eight square surns G5. Jacobi's identity and q-difference equations Chapter H. Congruence Properties of Partition Function Hl. Proof of p(5n + 4) = O (rnod 5) H2. Generating function for p(5n + 4) H3. Proof of p(7n + 5) O (rnod 7) H4. Generating function for p(7n + 6) H5. Proof of p(l1n + 6) O (rnod 11

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Problems and Solutions

College Mathematics Journal, 2005

Triple product sums of Catalan triangle numbers

Contributions to Discrete Mathematics, Jul 30, 2020

By means of quadratic transformations for the well-poised hypergeometric series, several reductio... more

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Iteration process for multiple rogers–ramanujan identities

Ukrainian Mathematical Journal, Jun 1, 2012

Replacing the monomials by an arbitrary sequence in the recursive lemma found by Bressoud (1983),... more Replacing the monomials by an arbitrary sequence in the recursive lemma found by Bressoud (1983), we establish several general transformation formulas from unilateral multiple basic hypergeometric series to bilateral univariate ones, which are then used for the derivation of numerous multiple series identities of Rogers -Ramanujan type. За допомогою замiни мономiв довiльною послiдовнiстю в рекурентнiй лемi Брессо (1983) встановлено декiлька загальних формул перетворення однобiчних кратних основних гiпергеометричних рядiв у двобiчнi одновимiрнi ряди, якi потiм використовуються для виведення численних тотожностей типу Роджерса -Рамануджана для кратних рядiв.

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Partial Fractions and q-Binomial Determinant Identities

Cubo, 2010

Partial fraction decomposition method is applied to evaluate a general determinant of shifted fac... more

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Inversion Techniques and Combinatorial Identities: Balanced Hypergeometric Series

Rocky Mountain Journal of Mathematics, Jun 1, 2002

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Inversion techniques and combinatorial identities. Basic hypergeometric identities

Publicationes Mathematicae Debrecen, Apr 1, 1994

Based on Carlitz' q-analogue of the Gould-Hsu inverse series relations, a new insight into basic ... more

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$Research paper thumbnail of New identities for terminating balanced $$_4\phi _3$$-series$

New identities for terminating balanced $$_4\phi _3$$-series

Journal of Algebraic Combinatorics, Jun 3, 2019

The duplicate form of the Carlitz inversions is employed to prove new identities for terminating ... more

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Four Variants of Riemann Zeta Function

Mathematics, Aug 19, 2022

By means of the generating function method and Dougall's formulae for bilateral hypergeometric se... more By means of the generating function method and Dougall's formulae for bilateral hypergeometric series, we examine four classes of infinite series, which may be considered as variants of Riemann zeta function. Several summation formulae are established in closed form, which shows remarkably that the values of these series result in multiples of integer powers of π either by rational numbers or by algebraic numbers.

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q-binomial formulae of Dixon`s type and the Fibonomial sums

Applicable Analysis and Discrete Mathematics, 2020

Cubic sums of the Gaussian q-binomial coefficients with certain weight functions will be evaluate... more Cubic sums of the Gaussian q-binomial coefficients with certain weight functions will be evaluated in this paper. To realize this, we will derive two remarkable formulae by means of the Carlitz-Sears transformation on terminating well-poised q-series. As consequences, several summation formulae on Fibonomial coefficients are presented by specializing the value of base q in our q-series identities.

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Evaluation of Infinite Series by Integrals

Mathematics, Jul 13, 2022

We examine a large class of infinite triple series and establish a general summation formula. Thi... more We examine a large class of infinite triple series and establish a general summation formula. This is done by expressing the triple series in terms of definite integrals involving arctangent function that are evaluated in turn in closed forms. Numerous explicit formulae are tabulated for the triple series whose values result in elegant expressions as π, ln 2 and the Catalan constant G.

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Evaluating a class of balanced q -series

Turkish Journal of Mathematics, Sep 9, 2018

By means of the modified Abel lemma on summation by parts, we examine a class of terminating bala... more

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Abel’s method on summation by parts and balanced q-series identities

Applicable Analysis and Discrete Mathematics, 2010

The Abel method on summation by parts is reformulated to present new and elementary proofs of sev... more The Abel method on summation by parts is reformulated to present new and elementary proofs of several classical identities of terminating balanced basic hypergeometric series. The examples strengthen our conviction that as traditional analytical instrument, the revised Abel method on summation by parts is indeed a very natural choice for working with basic hypergeometric series. A k-1 B k .

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Triplicate Dual Series of Dougall-Dixon Theorem

arXiv (Cornell University), Apr 4, 2021

Applying the triplicate form of the extended Gould-Hsu inverse series relations to Dougall's summ... more

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$Research paper thumbnail of $q$-Analogues of $\pi$-Series by Applying Carlitz Inversions to $q$-Pfaff-Saalsch{\"u}tz Theorem$

$q$-Analogues of $\pi$-Series by Applying Carlitz Inversions to $q$-Pfaff-Saalsch{\"u}tz Theorem

arXiv (Cornell University), Feb 24, 2021

By applying multiplicate forms of the Carlitz inverse series relations to the q-Pfaff-Saalschütz ... more By applying multiplicate forms of the Carlitz inverse series relations to the q-Pfaff-Saalschütz summation theorem, we establish twenty five nonterminating q-series identities with several of them serving as q-analogues of infinite series expressions for π and 1/π, including some typical ones discovered by and Guillera.

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Alternating series of Apéry-type for the Riemann zeta function

Contributions to Discrete Mathematics, Dec 22, 2020

By making use of a transformation formula for the nonterminating well-poised 5F4-series, we inves... more

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Alternating Convolutions of Catalan Numbers

arXiv (Cornell University), May 2, 2020

A new class of alternating convolutions concerning binomial coefficients and Catalan numbers are ... more

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Integrals of hyperbolic tangent function

Discrete mathematics letters, Apr 6, 2024

By means of the contour integration method, we evaluate, in closed form, a class of definite inte... more

Download

TERMINATING ALMOST POISED q-DIXON SUMS

Kyushu Journal of Mathematics

By means of the linearization method and the Carlitz-Sears transformation, the terminating almost... more

Download

Infinite Series Concerning Tails of Riemann Zeta Values

Axioms, Aug 2, 2023

Download

Basic Hypergeometric Series

Quaderni di Matematica, 2004

Download

Problems and Solutions

College Mathematics Journal, 2005

Triple product sums of Catalan triangle numbers

Contributions to Discrete Mathematics, Jul 30, 2020

By means of quadratic transformations for the well-poised hypergeometric series, several reductio... more

Download

Iteration process for multiple rogers–ramanujan identities

Ukrainian Mathematical Journal, Jun 1, 2012

Download

Partial Fractions and q-Binomial Determinant Identities

Cubo, 2010

Partial fraction decomposition method is applied to evaluate a general determinant of shifted fac... more

Download

Inversion Techniques and Combinatorial Identities: Balanced Hypergeometric Series

Rocky Mountain Journal of Mathematics, Jun 1, 2002

Download

Inversion techniques and combinatorial identities. Basic hypergeometric identities

Publicationes Mathematicae Debrecen, Apr 1, 1994

Based on Carlitz' q-analogue of the Gould-Hsu inverse series relations, a new insight into basic ... more

Download

$Research paper thumbnail of New identities for terminating balanced $$_4\phi _3$$-series$

New identities for terminating balanced $$_4\phi _3$$-series

Journal of Algebraic Combinatorics, Jun 3, 2019

The duplicate form of the Carlitz inversions is employed to prove new identities for terminating ... more

Download

Four Variants of Riemann Zeta Function

Mathematics, Aug 19, 2022

Download

q-binomial formulae of Dixon`s type and the Fibonomial sums

Applicable Analysis and Discrete Mathematics, 2020

Download

Evaluation of Infinite Series by Integrals

Mathematics, Jul 13, 2022

Download

Evaluating a class of balanced q -series

Turkish Journal of Mathematics, Sep 9, 2018

By means of the modified Abel lemma on summation by parts, we examine a class of terminating bala... more

Download

Abel’s method on summation by parts and balanced q-series identities

Applicable Analysis and Discrete Mathematics, 2010

Download

Triplicate Dual Series of Dougall-Dixon Theorem

arXiv (Cornell University), Apr 4, 2021

Applying the triplicate form of the extended Gould-Hsu inverse series relations to Dougall's summ... more

Download

$Research paper thumbnail of $q$-Analogues of $\pi$-Series by Applying Carlitz Inversions to $q$-Pfaff-Saalsch{\"u}tz Theorem$

$q$-Analogues of $\pi$-Series by Applying Carlitz Inversions to $q$-Pfaff-Saalsch{\"u}tz Theorem

arXiv (Cornell University), Feb 24, 2021

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Alternating series of Apéry-type for the Riemann zeta function

Contributions to Discrete Mathematics, Dec 22, 2020

By making use of a transformation formula for the nonterminating well-poised 5F4-series, we inves... more

Download

Alternating Convolutions of Catalan Numbers

arXiv (Cornell University), May 2, 2020

A new class of alternating convolutions concerning binomial coefficients and Catalan numbers are ... more

Download

Wenchang Chu

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