Results 21 to 30 of about 6,635 (118)
Two-Variable q-Hermite-Based Appell Polynomials and Their Applications
MathematicsA noteworthy advancement within the discipline of q-special function analysis involves the extension of the concept of the monomiality principle to q-special polynomials.
Mohammed Fadel +2 more
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Two-parameter identities for \(q\)-Appell polynomials
, 2023 Summary: In this paper, by using the techniques of the \(q\)-exponential generating series, we extend a well-known two-parameter identity for the Appell polynomials to the \(q\)-Appell polynomials of type I and II. More precisely, we obtain two different \(q\)-analogues of such an identity.
Munarini E.
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Multiplication formulas for q-Appell polynomials and the multiple q-power sums
Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica, 2016 In the first article on q-analogues of two Appell polynomials, the generalized Apostol-Bernoulli and Apostol-Euler polynomials, focus was on generalizations, symmetries, and complementary argument theorems. In this second article, we focus on a recent paper by Luo, and one paper on power sums by Wang and Wang.
Ernst, Thomas
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Finding the q-Appell Convolution of Certain Polynomials Within the Context of Quantum Calculus
MathematicsThis article introduces the theory of three-variable q-truncated exponential Gould–Hopper-based Appell polynomials by employing a generating function approach that incorporates q-calculus functions.
Waseem Ahmad Khan +4 more
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Journal of Inequalities and ApplicationsIn this paper, we attempt to use the Dunkl analog to study the convergence properties of q-Phillips operators by using the q-Appell polynomials. By applying the new sequences of continuous functions ν s , q ( z ) = ( z − 1 2 [ s ] q ) ϱ $\nu _{s,q}(z ...
Md. Nasiruzzaman +4 more
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Generalized Fubini Apostol‐Type Polynomials and Probabilistic Applications
International Journal of Mathematics and Mathematical Sciences, Volume 2022, Issue 1, 2022., 2022 The paper aims to introduce and investigate a new class of generalized Fubini‐type polynomials. The generating functions, special cases, and properties are introduced. Using the generating functions, various interesting identities, and relations are derived. Also, special polynomials are obtained from the general class of polynomials.
Rabab S. Gomaa +2 more
wiley +1 more source
The different tongues of q-calculus; pp. 81–99 [PDF]
Proceedings of the Estonian Academy of Sciences, 2008 In this review paper we summarize the various dialects of q-calculus: quantum calculus, time scales, and partitions. The close connection between Îq(x) functions on the one hand, and elliptic functions and theta functions on the other hand will be shown.
Thomas Ernst
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A New Class of Extended Hypergeometric Functions Related to Fractional Integration and Transforms
Journal of Mathematics, Volume 2022, Issue 1, 2022., 2022 The focus of this research is to use a new extended beta function and develop the extensions of Gauss hypergeometric functions and confluent hypergeometric function formulas that are presumed to be new. Four theorems have also been defined under the generalized fractional integral operators that provide an image formula for the extension of new Gauss ...
Vandana Palsaniya +4 more
wiley +1 more source
Two New Generalizations of Extended Bernoulli Polynomials and Numbers, and Umbral Calculus
Journal of Mathematics, Volume 2022, Issue 1, 2022., 2022 Among a remarkably large number of various extensions of polynomials and numbers, and diverse introductions of new polynomials and numbers, in this paper, we choose to introduce two new generalizations of some extended Bernoulli polynomials and numbers by using the Mittag–Leffler function and the confluent hypergeometric function.
Nabiullah Khan +4 more
wiley +1 more source
q-Differential equations for q-classical polynomials and q-Jacobi-Stirling numbers [PDF]
, 2016 We introduce, characterise and provide a combinatorial interpretation for the so-called q-Jacobi–Stirling numbers. This study is motivated by their key role in the (reciprocal) expansion of any power of a second order q-differential operator having the
Zeng, Jiang +5 more
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