Results 1 to 10 of about 485 (66)
On Elliptic and Hyperbolic Modular Functions and the Corresponding Gudermann Peeta Functions
Axioms, 2015 In this article, we move back almost 200 years to Christoph Gudermann, the great expert on elliptic functions, who successfully put the twelve Jacobi functions in a didactic setting. We prove the second hyperbolic series expansions for elliptic functions
Thomas Ernst
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Torus knots and quantum modular forms [PDF]
Research in the Mathematical Sciences, 2014 In this paper we compute a q-hypergeometric expression for the cyclotomic expansion of the colored Jones polynomial for the left-handed torus knot (2,2t+1). We use this to define a family of q-series, the simplest case of which is the generating function
K. Hikami, Jeremy Lovejoy
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On recursions for coefficients of mock theta functions [PDF]
Research in Number Theory, 2015 We use a generalized Lambert series identity due to the first author to present q-series proofs of recent results of Imamoğlu, Raum and Richter concerning recursive formulas for the coefficients of two 3rd order mock theta functions.
Song Heng Chan, Renrong Mao, R. Osburn
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Analytical properties of the two-variables Jacobi matrix polynomials with applications
Demonstratio Mathematica, 2021 In the current study, we introduce the two-variable analogue of Jacobi matrix polynomials. Some properties of these polynomials such as generating matrix functions, a Rodrigue-type formula and recurrence relations are also derived.
Abdalla Mohamed, Hidan Muajebah
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Starlike and convexity properties of q-Bessel-Struve functions
Demonstratio Mathematica, 2022 This paper introduces three different normalization associated with the second and third q-Bessel-Struve functions. We use Hadamard factorizations to determine the radii of starlike and convexity of these functions.
Oraby Karima M., Mansour Zeinab S. I.
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Partial Theta Functions. I. Beyond the Lost Notebook [PDF]
, 2001 It is shown how many of the partial theta function identities in Ramanujan's lost notebook can be generalized to infinite families of such identities.
S. Warnaar
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Further results on q-Lie groups, q-Lie algebras and q-homogeneous spaces
Special Matrices, 2021 We introduce most of the concepts for q-Lie algebras in a way independent of the base field K. Again it turns out that we can keep the same Lie algebra with a small modification.
Ernst Thomas
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A bilateral extension of the q-Selberg integral [PDF]
, 2013 A multi-dimensional bilateral q-series extending the q-Selberg integral is studied using concepts of truncation, regularization and connection formulae.
Masahiko Ito, P. Forrester
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An inequality for q-integral and its applications
Journal of Inequalities and Applications, 2014 In this paper, we use the q-binomial theorem to establish an inequality for the q-integral. As applications of the inequality, we give some sufficient conditions for convergence of the q-integral. MSC:26D15, 33D15.
Mingjin Wang
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MOCK THETA FUNCTIONS AND QUANTUM MODULAR FORMS
Forum of Mathematics, Pi, 2013 Ramanujan’s last letter to Hardy concerns the asymptotic properties of modular forms and his ‘mock theta functions’. For the mock theta function $f(q)$, Ramanujan claims that as $q$ approaches an even-order $2k$ root of unity, we have $$\begin{eqnarray ...
AMANDA FOLSOM +2 more
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