53 citations · 618 across the 64 of their papers we have counts for
28 papers · 1 filter
Well-poised basic q-Taylor expansions with complementary remainders and a two-basis kernel
Abdulhafeez A. Abdulsalam, Michael J. Schlosser
We prove a nonterminating well-poised basic -Taylor expansion with complementary remainders for a two-basis infinite-product kernel implicitly proposed by the second author in \…
Multidimensional Matrix Inversions and Elliptic Hypergeometric Series on Root Systems
Hjalmar Rosengren, Michael J. Schlosser
Multidimensional matrix inversions provide a powerful tool for studying multiple hypergeometric series. In order to extend this technique to elliptic hypergeometric series, we pres…
Log-concavity results for a biparametric and an elliptic extension of the -binomial coefficients
Michael J. Schlosser, Koushik Senapati, Ali K. Uncu
We establish discrete and continuous log-concavity results for a biparametric extension of the -numbers and of the -binomial coefficients. By using classical results for the…
Hypergeometric and basic hypergeometric series and integrals associated with root systems
Michael J. Schlosser
We give an overview of some of the main results from the theories of hypergeometric and basic hypergeometric series and integrals associated with root systems. In particular, we li…
Elliptic Well-Poised Bailey Transforms and Lemmas on Root Systems
Gaurav Bhatnagar, Michael J. Schlosser
We list , and extensions of the elliptic WP Bailey transform and lemma, given for by Andrews and Spiridonov. Our work requires multiple series extensions of…
-Analogues of two product formulas of hypergeometric functions by Bailey
Michael J. Schlosser
We use Andrews' -analogues of Watson's and Whipple's summation theorems to deduce two formulas for products of specific basic hypergeometric functions. These constitute…
Elliptic Hypergeometric Summations by Taylor Series Expansion and Interpolation
Michael J. Schlosser, Meesue Yoo
We use elliptic Taylor series expansions and interpolation to deduce a number of summations for elliptic hypergeometric series. We extend to the well-poised elliptic case results t…
Multiple hypergeometric series -- Appell series and beyond
Michael J. Schlosser
This survey article (which will appear as a chapter in the book ``Computer Algebra in Quantum Field Theory: Integration, Summation and Special Functions'', Springer-Verlag) provide…
On an identity by Chaundy and Bullard. II. More history
Tom H. Koornwinder, Michael J. Schlosser
An identity by Chaundy and Bullard writes 1/(1-x)^n (n=1,2,...) as a sum of two truncated binomial series. In a paper which appeared in 2008 in Indag. Math. the authors surveyed ma…
Theta Functions, Elliptic Hypergeometric Series, and Kawanaka's Macdonald Polynomial Conjecture
Robin Langer, Michael J. Schlosser, S. Ole Warnaar
We give a new theta-function identity, a special case of which is utilised to prove Kawanaka's Macdonald polynomial conjecture. The theta-function identity further yields a transfo…
On an identity by Chaundy and Bullard. I
Tom H. Koornwinder, Michael J. Schlosser
An identity by Chaundy and Bullard writes 1/(1-x)^n (n=1,2,...) as a sum of two truncated binomial series. This identity was rediscovered many times. Notably, a special case was re…
Multilateral inversion of A_r, C_r and D_r basic hypergeometric series
Michael J. Schlosser
In [Electron. J. Combin. 10 (2003), #R10], the author presented a new basic hypergeometric matrix inverse with applications to bilateral basic hypergeometric series. This matrix in…
Curious extensions of Ramanujan's 1-psi-1 summation formula
Victor J. W. Guo, Michael J. Schlosser
We deduce new q-series identities by applying inverse relations to certain identities for basic hypergeometric series. The identities obtained themselves do not belong to the hiera…
A new multivariable 6-psi-6 summation formula
Michael Schlosser
By multidimensional matrix inversion, combined with an A_r extension of Jackson's 8-phi-7 summation formula by Milne, a new multivariable 8-phi-7 summation is derived. By a polynom…
Summation, transformation, and expansion formulas for multibasic theta hypergeometric series
George Gasper, Michael Schlosser
After reviewing some fundamental facts from the theory of theta hypergeometric series we derive, using indefinite summation, several summation, transformation, and expansion formul…
Elliptic determinant evaluations and the Macdonald identities for affine root systems
Hjalmar Rosengren, Michael Schlosser
We obtain several determinant evaluations, related to affine root systems, which provide elliptic extensions of Weyl denominator formulas. Some of these are new, also in the polyno…
Noncommutative extensions of Ramanujan's 1-psi-1 summation
Michael Schlosser
Using functional equations, we derive noncommutative extensions of Ramanujan's 1-psi-1 summation.
Summation formulae for noncommutative hypergeometric series
Michael Schlosser
We establish several summation formulae for hypergeometric and basic hypergeometric series involving noncommutative parameters and argument. These results were inspired by a recent…
Some curious q-series expansions and beta integral evaluations
George Gasper, Michael Schlosser
We deduce several curious q-series expansions by applying inverse relations to certain identities for basic hypergeometric series. After rewriting some of these expansions in terms…
Another proof of Bailey's 6-psi-6 summation
Frederic Jouhet, Michael Schlosser
Adapting a method used by Cauchy, Bailey, Slater, and more recently, the second author, we give a new proof of Bailey's celebrated 6-psi-6 summation formula.
On Warnaar's elliptic matrix inversion and Karlsson-Minton-type elliptic hypergeometric series
Hjalmar Rosengren, Michael Schlosser
Using Krattenthaler's operator method, we give a new proof of Warnaar's recent elliptic extension of Krattenthaler's matrix inversion. Further, using a theta function identity clos…
Summations and transformations for multiple basic and elliptic hypergeometric series by determinant evaluations
Hjalmar Rosengren, Michael Schlosser
Using multiple q-integrals and a determinant evaluation, we establish a multivariable extension of Bailey's nonterminating 10-phi-9 transformation. From this result, we deduce new…
A nonterminating 8-phi-7 summation for the root system C_r
Michael J. Schlosser
Using multiple q-integrals and a determinant evaluation, we establish a nonterminating 8-phi-7 summation for the root system C_r. We also give some important specializations explic…
Inversion of bilateral basic hypergeometric series
Michael Schlosser
We present a new matrix inverse with applications in the theory of bilateral basic hypergeometric series. Our matrix inversion result is directly extracted from an instance of Bail…