Found 1,721 Documents (Results 1–100)
Some parametric \(q\)-supercongruences from a summation of Gasper and Rahman. (English) Zbl 07928596
Reviewer: Guo-Shuai Mao (Nanjing)
Formal (\(q\)-)Euler integrals over the unit hypercube and over triangles in higher dimensions for multiple (\(q\)-)hypergeometric functions. (English) Zbl 07927149
Some observations on Lambert series, vanishing coefficients and dissections of infinite products and series. (English) Zbl 07924587
Andrews, George E. (ed.) et al., Analytic and combinatorial number theory: the legacy of Ramanujan. Contributions in honor of Bruce C. Berndt. Selected papers based on the presentations at the conference, Champaign, IL, USA, June 6–9, 2019. Singapore: World Scientific. Monogr. Number Theory 12, 467-485 (2024).
On conjectures of Koike and Somos for modular identities for the Rogers-Ramanujan functions. (English) Zbl 07924572
Andrews, George E. (ed.) et al., Analytic and combinatorial number theory: the legacy of Ramanujan. Contributions in honor of Bruce C. Berndt. Selected papers based on the presentations at the conference, Champaign, IL, USA, June 6–9, 2019. Singapore: World Scientific. Monogr. Number Theory 12, 223-260 (2024).
Hankel determinants of linear combinations of moments of orthogonal polynomials. (English) Zbl 07924567
Andrews, George E. (ed.) et al., Analytic and combinatorial number theory: the legacy of Ramanujan. Contributions in honor of Bruce C. Berndt. Selected papers based on the presentations at the conference, Champaign, IL, USA, June 6–9, 2019. Singapore: World Scientific. Monogr. Number Theory 12, 129-157 (2024).
Two curious \(q\)-supercongruences and their extensions. (English) Zbl 07920525
Reviewer: Marcel G. de Bruin (Heemstede)
Supercongruences arising from a \({}_7 F_6\) hypergeometric transformation formula. (English) Zbl 07920509
Rogers-Ramanujan type identities involving double, triple and quadruple sums. (English) Zbl 07920332
\(q\)-deformed coherent states associated with the sequence \(x_n^{q,\alpha}=(1+\alpha q^{n-1})[n]_q\). (English) Zbl 07910995
On evaluations of the cubic continued fraction by modular equations of degree 3 revisited. (English) Zbl 07902306
Generalizations of the Jacobi identity to the case of the Lauricella function \(F_D^{(N)}\). (English) Zbl 07901588
New \(q\)-analogues of Van Hamme’s (F.2) supercongruence and of some related supercongruences. (English) Zbl 1543.33012
Explicit forms and proofs of Zagier’s rank three examples for Nahm’s problem. (English) Zbl 07872171
Formulas for \(p\)-adic \(q\)-integrals including falling-rising factorials, combinatorial sums and special numbers. (English) Zbl 1543.11106
Cyclotomic valuation of \(q\)-Pochhammer symbols and \(q\)-integrality of basic hypergeometric series. (English) Zbl 07856592
Reviewer: Zhi-Guo Liu (Shanghai)
Symmetric function generalizations of the \(q\)-Baker-Forrester ex-conjecture and Selberg-type integrals. (English) Zbl 1540.05170
Some \(q\)-supercongruences for double and triple basic hypergeometric series. (English) Zbl 1539.11014
Series involving cubic central binomial coefficients of convergence rate 1/64. (English) Zbl 07842728
Proof of two supercongruences of truncated hypergeometric series \({}_4 F_3\). (English) Zbl 1539.11010
Generating functions for polynomials derived from central moments involving Bernstein basis functions and their applications. (English) Zbl 1535.11166
On a conjectural series of Sun for the mathematical constant \(\beta(4)\). (English) Zbl 07834228
Reviewer: Thomas Ernst (Uppsala)
Multiple orthogonal polynomials, \(d\)-orthogonal polynomials, production matrices, and branched continued fractions. (English) Zbl 1536.42027
Infinite series of convergence rate \(-1/8\) suggested by two formulae of Guillera. (English) Zbl 07828400
Factors of certain basic hypergeometric sums. (English) Zbl 1536.33017
Reviewer: Navneet Lal Sharma (Vadodara)
Several identities and relations related to \(q\)-analogues of Pochhammer \(k\)-symbol with applications to Fuss-Catalan-Qi numbers. (English) Zbl 07822266
On \(_{5} \psi_{5}\) identities of Bailey. (English) Zbl 1539.33014
Reviewer: Uğur Duran (İskenderun)
A new extension of a “divergent” Ramanujan-type supercongruence. (English) Zbl 1536.33016
Reviewer: Rózsa Horváth-Bokor (Budakalász)
Two-variable \(q\)-Laguerre polynomials from the context of quasi-monomiality. (English) Zbl 1537.33022
Reviewer: Roberto S. Costas-Santos (Sevilla)
\(q\)-supercongruences from Jackson’s \({}_8 \phi_7\) summation and Watson’s \({}_8 \phi_7\) transformation. (English) Zbl 1536.11008
Reviewer: Enzo Bonacci (Latina)
Generalizations of the (F.2) supercongruence of Van Hamme. (English) Zbl 1535.33021
Reviewer: Uğur Duran (İskenderun)
On some \(\Pi_q\)-identities of Gosper. (English) Zbl 1534.33014
Reviewer: Rózsa Horváth-Bokor (Budakalász)
Enumeration of anti-invariant subspaces and Touchard’s formula for the entries of the \(q\)-Hermite Catalan matrix. (English) Zbl 1530.05009
Supercongruences involving Domb numbers and binary quadratic forms. (English) Zbl 1530.11004
Reviewer: Enzo Bonacci (Latina)
Identities for the Rogers-Ramanujan Continued Fraction. arXiv:2410.17110
Preprint, arXiv:2410.17110 [math.NT] (2024).
A remark on modular equations involving Rogers-Ramanujan continued fraction via \(5\)-dissections. arXiv:2410.14149
Preprint, arXiv:2410.14149 [math.NT] (2024).
One variable Generalization of five entries of Ramanujan and their finite analogue. arXiv:2410.13430
Preprint, arXiv:2410.13430 [math.NT] (2024).
\(q\)-Binomial Identities Finder. arXiv:2408.00186
Preprint, arXiv:2408.00186 [math.CO] (2024).
Mizuno’s rank three Nahm sums II: identities of index \((1,2,2)\) and modular forms. arXiv:2407.21725
Preprint, arXiv:2407.21725 [math.NT] (2024).
A remarkable basic hypergeometric identity. arXiv:2406.02954
Preprint, arXiv:2406.02954 [math.NT] (2024).
A divisor generating q-series identity and its applications to probability theory and random graphs. arXiv:2405.01877
Preprint, arXiv:2405.01877 [math.NT] (2024).
Wilf-Zeilberger seeds: \(q\)-analogues. arXiv:2403.04555
Preprint, arXiv:2403.04555 [math.CO] (2024).
On q-series and the moment problem associated to local factors. arXiv:2403.01247
Preprint, arXiv:2403.01247 [math.NT] (2024).
Mizuno’s rank three Nahm sums I: identities of index \((1,1,2)\). arXiv:2402.06253
Preprint, arXiv:2402.06253 [math.NT] (2024).
On the identities of Ramanujan – a \(q\)-series approach. (English) Zbl 1540.33018
Reviewer: Rózsa Horváth-Bokor (Budakalász)
On generalized \(q\)-hyperbolic functions in the spirit of Kapteyn, with corresponding \(q\)-Lie group. (English) Zbl 1542.33019
Silvestrov, Sergei (ed.) et al., Non-commutative and non-associative algebra and analysis structures. SPAS 2019. Selected papers based on the presentations at the international conference on stochastic processes and algebraic structures – from theory towards applications, Västerås, Sweden, September 30 – October 2, 2019. Cham: Springer. Springer Proc. Math. Stat. 426, 285-301 (2023).
Reviewer: Toufik Mansour (Haifa)
Summation formulas on harmonic numbers and five central binomial coefficients. (English) Zbl 07820501
A new class of Laguerre-based Frobenius type Eulerian numbers and polynomials. (English) Zbl 07805663
\(q\)-analogues of \(\pi \)-series by applying Carlitz inversions to \(q\)-Pfaff-Saalschütz theorem. (English) Zbl 1535.33018
Reviewer: Roberto S. Costas-Santos (Sevilla)
Identities of a general multiple Hurwitz-Lerch zeta function and applications. (English) Zbl 1538.11152
Certain summation formulae and relations due to double series associated with the general hypergeometric type Hurwitz-Lerch zeta functions. (English) Zbl 1538.11151
Relations and identities due to double series associated with general Hurwitz-Lerch type zeta functions. (English) Zbl 1538.11154
Some identities of certain basic hypergeometric series and their applications to mock theta functions. (English) Zbl 1536.33021
Reviewer: Marcel G. de Bruin (Heemstede)
Three families of \(q\)-supercongruences from a quadratic transformation of Rahman. (English) Zbl 1535.33019
Reviewer: Marcel G. de Bruin (Heemstede)
A new \(q\)-analogue of Van Hamme’s (G.2) supercongruence for primes \(p\equiv 3\pmod{4}\). (English) Zbl 1532.33030
Generalizations of mock theta functions and Appell-Lerch sums. (English) Zbl 1539.33013
Reviewer: Navneet Lal Sharma (Vadodara)
Lattice paths and branched continued fractions: an infinite sequence of generalizations of the Stieltjes-Rogers and Thron-Rogers polynomials, with coefficientwise Hankel-total positivity. (English) Zbl 1528.05001
Memoirs of the American Mathematical Society 1450. Providence, RI: American Mathematical Society (AMS) (ISBN 978-1-4704-6268-0/pbk; 978-1-4704-7683-0/ebook). v, 154 p. (2023).
MSC:
05-02
33-02
05A15
05A19
42C05
33C05
33C20
33D05
05A20
05C30
05E05
15B05
15B48
30B70
30E05
44A60
11B68
11A55
11B75
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