Michael J. Schlosser
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
Research Subjects
Michael J. Schlosser has a total of 32 co-authors. Here are the top co-authors by number of shared publications:
- Victor J. W. Guo
School of Mathematics, Hangzhou Normal University, Hangzhou 311121, P. R. China
17 shared publications - Gaurav Bhatnagar
Indian Institute of Technology Jodhpur
5 shared publications Meesue Yoo
Department of Mathematics, Chungbuk National University, Cheongju 28644, South Korea
5 shared publications- Meesue Yoo
Fakultät für Mathematik Universität Wien Oskar-Morgenstern-Platz 1 A-1090 Vienna Austria
5 shared publications - Meesue Yoo
Department of Mathematics, Chungbuk National University, Cheongju, South Korea
4 shared publications - Nian Hong Zhou
Guangxi Normal University
4 shared publications
Latest Publications
- Open Access
- 18 October 2026
- Published by Taylor & Francis in Integral Transforms and Special Functions
- p. 1-40
Signed generalized Stirling polynomials, nested sums, and hyperbolic secant integral identities
- 18 October 2026
- Published by Taylor & Francis in Integral Transforms and Special Functions
- p. 1-40
Open AccessSigned generalized Stirling polynomials, nested sums, and hyperbolic secant integral identities
- Open Access
- 18 August 2026
- Published by Springer Nature in The Ramanujan Journal
- Vol. 70 (4) , 72
Product formulas for basic hypergeometric series by evaluations of Askey–Wilson polynomials
Ismail and Wilson derived a generating function for Askey–Wilson polynomials which is given by a product of q -Gauss (Heine) nonterminating basic hypergeometric functions. We provide a generalization of that generating function which contains an extra parameter. A special case gives a closed form summation formula for a quadruple basic hypergeometric sum. We further present new terminating balanced $${\phantom {a}}_4\phi _3$$ summations that give rise to q -quadratic special values for Askey–Wilson polynomials. We also similarly present new terminating 2-balanced and 3-balanced $${\phantom {a}}_4\phi _3$$ summations. Using the Ismail–Wilson generating function combined with explicit summations for terminating balanced basic hypergeometric $${\phantom {a}}_4\phi _3$$ series, we compute new basic hypergeometric product transformations for nonterminating basic hypergeometric series and provide corresponding integral representations. Further new identities are obtained by applying Cayley–Orr type expansion formulas.- 18 August 2026
- Published by Springer Nature in The Ramanujan Journal
- Vol. 70 (4) , 72
Open AccessProduct formulas for basic hypergeometric series by evaluations of Askey–Wilson polynomials
Ismail and Wilson derived a generating function for Askey–Wilson polynomials which is given by a product of q -Gauss (Heine) nonterminating basic hypergeometric functions. We provide a generalization of that generating function which contains an extra parameter. A special case gives a closed form summation formula for a quadruple basic hypergeometric sum. We further present new terminating balanced $${\phantom {a}}_4\phi _3$$ summations that give rise to q -quadratic special values for Askey–Wilson polynomials. We also similarly present new terminating 2-balanced and 3-balanced $${\phantom {a}}_4\phi _3$$ summations. Using the Ismail–Wilson generating function combined with explicit summations for terminating balanced basic hypergeometric $${\phantom {a}}_4\phi _3$$ series, we compute new basic hypergeometric product transformations for nonterminating basic hypergeometric series and provide corresponding integral representations. Further new identities are obtained by applying Cayley–Orr type expansion formulas. - Open Access
- 20 June 2026
- Published by Springer Nature in Arabian Journal of Mathematics
- Vol. 15 (2) , 643-668
Transformations and Summations for Bilateral Basic Hypergeometric Series
We review and derive transformation and summation formulas for bilateral basic hypergeometric series. Our study focuses on consequences of certain bilateral extensions of two important results by Bailey, namely a transformation for very-well-poised $$_8\!W_7$$ series in terms of two balanced $$_4\phi _3$$ series, and a transformation connecting three $$_8\!W_7$$ series. Two rather recently discovered transformations of bilateral basic very-well-poised $${}_8\!\Psi _8$$ , one by Zhang and Zhang, the other by Wei and Yu, serve as the starting point of our investigations. From these transformations we work out interesting special cases that were not considered before, including explicit bilateral quadratic and cubic summations. We further explicitly record noteworthy lower-level transformations derived by taking suitable limits and deduce more transformations by exploiting the symmetry of the parameters in the series.- 20 June 2026
- Published by Springer Nature in Arabian Journal of Mathematics
- Vol. 15 (2) , 643-668
Open AccessTransformations and Summations for Bilateral Basic Hypergeometric Series
We review and derive transformation and summation formulas for bilateral basic hypergeometric series. Our study focuses on consequences of certain bilateral extensions of two important results by Bailey, namely a transformation for very-well-poised $$_8\!W_7$$ series in terms of two balanced $$_4\phi _3$$ series, and a transformation connecting three $$_8\!W_7$$ series. Two rather recently discovered transformations of bilateral basic very-well-poised $${}_8\!\Psi _8$$ , one by Zhang and Zhang, the other by Wei and Yu, serve as the starting point of our investigations. From these transformations we work out interesting special cases that were not considered before, including explicit bilateral quadratic and cubic summations. We further explicitly record noteworthy lower-level transformations derived by taking suitable limits and deduce more transformations by exploiting the symmetry of the parameters in the series. - Open Access
- 2 February 2026
- Published by California Digital Library (CDL) in Combinatorial Theory
- Vol. 5 (4)
Diagonal operators, \(q\)-Whittaker functions and rook theoryWe discuss the problem posed by Bender, Coley, Robbins and Rumsey of enumerating the number of subspaces which have a given profile with respect to a linear operator over the finite field F q. We solve this problem in the case where the operator is diagonalizable. The solution leads us to a new class of polynomials b µν (q) indexed by pairs of integer partitions. These polynomials have several interesting specializations and can be expressed as positive sums over semistandard tableaux. We present a new correspondence between set partitions and semistandard tableaux. A close analysis of this correspondence reveals the existence of several new set partition statistics which generate the polynomials b µν (q); each such statistic arises from a Mahonian statistic on multiset permutations. The polynomials b µν (q) are also given a description in terms of coefficients in the monomial expansion of q-Whittaker symmetric functions which are specializations of Macdonald polynomials. We express the Touchard-Riordan generating polynomial for chord diagrams by number of crossings in terms of q-Whittaker functions. We also introduce a class of q-Stirling numbers defined in terms of the polynomials b µν (q) and present connections with q-rook theory in the spirit of Garsia and Remmel.
- 2 February 2026
- Published by California Digital Library (CDL) in Combinatorial Theory
- Vol. 5 (4)
Open AccessDiagonal operators, \(q\)-Whittaker functions and rook theoryWe discuss the problem posed by Bender, Coley, Robbins and Rumsey of enumerating the number of subspaces which have a given profile with respect to a linear operator over the finite field F q. We solve this problem in the case where the operator is diagonalizable. The solution leads us to a new class of polynomials b µν (q) indexed by pairs of integer partitions. These polynomials have several interesting specializations and can be expressed as positive sums over semistandard tableaux. We present a new correspondence between set partitions and semistandard tableaux. A close analysis of this correspondence reveals the existence of several new set partition statistics which generate the polynomials b µν (q); each such statistic arises from a Mahonian statistic on multiset permutations. The polynomials b µν (q) are also given a description in terms of coefficients in the monomial expansion of q-Whittaker symmetric functions which are specializations of Macdonald polynomials. We express the Touchard-Riordan generating polynomial for chord diagrams by number of crossings in terms of q-Whittaker functions. We also introduce a class of q-Stirling numbers defined in terms of the polynomials b µν (q) and present connections with q-rook theory in the spirit of Garsia and Remmel.
- Open Access
- 15 July 2025
- Published by New Zealand Journal of Mathematics Committee in New Zealand Journal of Mathematics
- Vol. 56, 15-32
An esoteric identity with many parameters and other elliptic extensions of elementary identities
We provide elliptic extensions of elementary identities such as the sum of the first $n$ odd or even numbers, the geometric sum and the sum of the first $n$ cubes. Many such identities, and their $q$-analogues, are indefinite sums, and can be obtained from telescoping. So we used telescoping in our study to find elliptic extensions of these identities. In the course of our study, we obtained an identity with many parameters, which appears to be new even in the $q$-case. In addition, we recover some $q$-identities due to Warnaar.- 15 July 2025
- Published by New Zealand Journal of Mathematics Committee in New Zealand Journal of Mathematics
- Vol. 56, 15-32
Open AccessAn esoteric identity with many parameters and other elliptic extensions of elementary identities
We provide elliptic extensions of elementary identities such as the sum of the first $n$ odd or even numbers, the geometric sum and the sum of the first $n$ cubes. Many such identities, and their $q$-analogues, are indefinite sums, and can be obtained from telescoping. So we used telescoping in our study to find elliptic extensions of these identities. In the course of our study, we obtained an identity with many parameters, which appears to be new even in the $q$-case. In addition, we recover some $q$-identities due to Warnaar. - Open Access
- 6 July 2025
- Published by SIGMA (Symmetry, Integrability and Geometry: Methods and Application) in Symmetry, Integrability and Geometry: Methods and Applications
- Vol. 21, 052
An Algebra of Elliptic Commuting Variables and an Elliptic Extension of the Multinomial Theorem
We introduce an algebra of elliptic commuting variables involving a base $q$, nome $p$, and $2r$ noncommuting variables. This algebra, which for $r=1$ reduces to an algebra considered earlier by the author, is an elliptic extension of the well-known algebra of $r$ $q$-commuting variables. We present a multinomial theorem valid as an identity in this algebra, hereby extending the author's previously obtained elliptic binomial theorem to higher rank. Two essential ingredients are a consistency relation satisfied by the elliptic weights and the Weierstraß type $\mathsf A$ elliptic partial fraction decomposition. From the elliptic multinomial theorem we obtain, by convolution, an identity equivalent to Rosengren's type $\mathsf A$ extension of the Frenkel-Turaev ${}_{10}V_9$ summation. Interpreted in terms of a weighted counting of lattice paths in the integer lattice $\mathbb Z^r$, this derivation of Rosengren's $\mathsf A_r$ Frenkel-Turaev summation constitutes the first combinatorial proof of that fundamental identity.- 6 July 2025
- Published by SIGMA (Symmetry, Integrability and Geometry: Methods and Application) in Symmetry, Integrability and Geometry: Methods and Applications
- Vol. 21, 052
Open AccessAn Algebra of Elliptic Commuting Variables and an Elliptic Extension of the Multinomial Theorem
We introduce an algebra of elliptic commuting variables involving a base $q$, nome $p$, and $2r$ noncommuting variables. This algebra, which for $r=1$ reduces to an algebra considered earlier by the author, is an elliptic extension of the well-known algebra of $r$ $q$-commuting variables. We present a multinomial theorem valid as an identity in this algebra, hereby extending the author's previously obtained elliptic binomial theorem to higher rank. Two essential ingredients are a consistency relation satisfied by the elliptic weights and the Weierstraß type $\mathsf A$ elliptic partial fraction decomposition. From the elliptic multinomial theorem we obtain, by convolution, an identity equivalent to Rosengren's type $\mathsf A$ extension of the Frenkel-Turaev ${}_{10}V_9$ summation. Interpreted in terms of a weighted counting of lattice paths in the integer lattice $\mathbb Z^r$, this derivation of Rosengren's $\mathsf A_r$ Frenkel-Turaev summation constitutes the first combinatorial proof of that fundamental identity. - Open Access
- 2 July 2025
- Published by Elsevier in Indagationes Mathematicae
- Vol. 36 (6) , 1762-1778
A family of orthogonal functions on the unit circle and a new multilateral matrix inverse
- 2 July 2025
- Published by Elsevier in Indagationes Mathematicae
- Vol. 36 (6) , 1762-1778
Open AccessA family of orthogonal functions on the unit circle and a new multilateral matrix inverse
- Open Access
- 10 April 2025
- Published by Springer Nature in Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales. Serie A. Matematicas
- Vol. 119 (2) , 1-10
A new family of q-hypergeometric congruences from Andrews’ multi-series transformation
We deduce a new family of q-hypergeometric congruences modulo the fourth power of a cyclotomic polynomial from George Andrews’ multi-series extension of the Watson transformation. A Karlsson–Minton type summation for very-well-poised basic hypergeometric series due to George Gasper also plays an important role in our proof. We put forward two relevant conjectures on supercongruences and q-supercongruences for further study.
- 10 April 2025
- Published by Springer Nature in Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales. Serie A. Matematicas
- Vol. 119 (2) , 1-10
Open AccessA new family of q-hypergeometric congruences from Andrews’ multi-series transformation
We deduce a new family of q-hypergeometric congruences modulo the fourth power of a cyclotomic polynomial from George Andrews’ multi-series extension of the Watson transformation. A Karlsson–Minton type summation for very-well-poised basic hypergeometric series due to George Gasper also plays an important role in our proof. We put forward two relevant conjectures on supercongruences and q-supercongruences for further study.
- Open Access
- 21 February 2025
- Published by Springer Nature in Research in the Mathematical Sciences
- Vol. 12 (1) , 1-19
Residue class biases in unrestricted partitions, partitions into distinct parts, and overpartitions
We prove specific biases in the number of occurrences of parts belonging to two different residue classes a and b, modulo a fixed nonnegative integer m, for the sets of unrestricted partitions, partitions into distinct parts, and overpartitions. These biases follow from inequalities for residue-weighted partition functions for the respective sets of partitions. We also establish asymptotic formulas for the numbers of partitions of size n that belong to these sets of partitions and have a symmetric residue class bias (i.e., for $$1\le a<m/2$$ and $$b=m-a$$ ), as n tends to infinity.- 21 February 2025
- Published by Springer Nature in Research in the Mathematical Sciences
- Vol. 12 (1) , 1-19
Open AccessResidue class biases in unrestricted partitions, partitions into distinct parts, and overpartitions
We prove specific biases in the number of occurrences of parts belonging to two different residue classes a and b, modulo a fixed nonnegative integer m, for the sets of unrestricted partitions, partitions into distinct parts, and overpartitions. These biases follow from inequalities for residue-weighted partition functions for the respective sets of partitions. We also establish asymptotic formulas for the numbers of partitions of size n that belong to these sets of partitions and have a symmetric residue class bias (i.e., for $$1\le a<m/2$$ and $$b=m-a$$ ), as n tends to infinity. - 20 September 2024
- Published by American Mathematical Society (AMS) in Proceedings of the American Mathematical Society
- Vol. 152 (11) , 4659-4673
Expansions of averaged truncations of basic hypergeometric series
Motivated by recent work of George Andrews and Mircea Merca [J. Combin. Theory Ser. A 119 (2012), pp. 1639–1643] on the expansion of the quotient of the truncation of Euler’s pentagonal number series by the complete series, we provide similar expansion results for averages involving truncations of selected, more general, basic hypergeometric series. In particular, our expansions include new results for averaged truncations of the series appearing in the Jacobi triple product identity, the q q -Gauß summation, and the very-well-poised 5 ϕ 5 {}_5\phi _5 summation. We show how special cases of our expansions can be used to recover various existing results. In addition, we establish new inequalities, such as one for a refinement of the number of partitions into three different colors.
- 20 September 2024
- Published by American Mathematical Society (AMS) in Proceedings of the American Mathematical Society
- Vol. 152 (11) , 4659-4673
Expansions of averaged truncations of basic hypergeometric series
Motivated by recent work of George Andrews and Mircea Merca [J. Combin. Theory Ser. A 119 (2012), pp. 1639–1643] on the expansion of the quotient of the truncation of Euler’s pentagonal number series by the complete series, we provide similar expansion results for averages involving truncations of selected, more general, basic hypergeometric series. In particular, our expansions include new results for averaged truncations of the series appearing in the Jacobi triple product identity, the q q -Gauß summation, and the very-well-poised 5 ϕ 5 {}_5\phi _5 summation. We show how special cases of our expansions can be used to recover various existing results. In addition, we establish new inequalities, such as one for a refinement of the number of partitions into three different colors.