Results 1 to 10 of about 437 (44)
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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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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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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On the q-exponential of matrix q-Lie algebras
Special Matrices, 2017 In this paper, we define several new concepts in the borderline between linear algebra, Lie groups and q-calculus.We first introduce the ring epimorphism r, the set of all inversions of the basis q, and then the important q-determinant and corresponding ...
Ernst Thomas
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A Connection Formula of the Hahn-Exton $q$-Bessel Function [PDF]
, 2011 We show a connection formula of the Hahn-Exton $q$-Bessel function around the origin and the infinity. We introduce the $q$-Borel transformation and the $q$-Laplace transformation following C. Zhang to obtain the connection formula. We consider the limit
Morita, Takeshi
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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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q-hypergeometric double sums as mock theta functions [PDF]
, 2012 Recently, Bringmann and Kane established two new Bailey pairs and used them to relate certain q-hypergeometric series to real quadratic fields. We show how these pairs give rise to new mock theta functions in the form of q-hypergeometric double sums ...
Andrews +5 more
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Hypergeometric $\tau$ Function of the $q$-Painlev\'e Systems of Type $(A_2+A_1)^{(1)}$ [PDF]
, 2010 We consider a $q$-Painlev\'e III equation and a $q$-Painlev\'e II equation arising from a birational representation of the affine Weyl group of type $(A_2+A_1)^{(1)}$.
Nakazono, Nobutaka
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On two 10th order mock theta identities
, 2013 We give short proofs of conjectural identities due to Gordon and McIntosh involving two 10th order mock theta functions.Comment: 5 pages, to appear in the Ramanujan ...
A. Folsom +8 more
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