Results 11 to 20 of about 444 (53)
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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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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On three theorems of Folsom, Ono and Rhoades
, 2013 In his deathbed letter to Hardy, Ramanujan gave a vague definition of a mock modular function: at each root of unity its asymptotics matches the one of a modular form, though a choice of the modular function depends on the root of unity. Recently Folsom,
Zudilin, Wadim
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Composition Formula for Saigo Fractional q‐Calculus Operator for the q‐Analogue of the H‐Function
International Journal of Mathematics and Mathematical Sciences, Volume 2026, Issue 1, 2026.The purpose of this paper is to investigate key properties of Saigo’s fractional q‐integral and q‐derivative operators involving the q‐analogue of Fox’s H‐function. We establish four main theorems describing the action of Saigo‐type fractional q‐operators on generalised power functions expressed in terms of the q‐Fox H‐function.
Arti Sharma +3 more
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Quantum Extensions of Widder’s Formula via q‐Deformed Calculus
Journal of Applied Mathematics, Volume 2025, Issue 1, 2025.In this study, we rigorously established q‐Widder’s formula of first and second kind by employing the q‐integral within a quantum calculus framework. Our approach introduces a novel formulation of the inverse q‐Laplace transform, enabling simplified computation without relying on conventional complex integration methods.
S. S. Naina Mohammed +6 more
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A simple proof of Bailey's very-well-poised 6-psi-6 summation
, 2000 We give elementary derivations of some classical summation formulae for bilateral (basic) hypergeometric series. In particular, we apply Gauss' 2-F-1 summation and elementary series manipulations to give a simple proof of Dougall's 2-H-2 summation ...
Schlosser, M.
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