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Combinatorial identities for Appell polynomials [PDF]
Applicable Analysis and Discrete Mathematics, 2018 Using the techniques of the modern umbral calculus, we derive several combinatorial identities involving s-Appell polynomials. In particular, we obtain identities for classical polynomials, such as the Hermite, Laguerre, Bernoulli, Euler, N?rlund, hypergeometric Bernoulli, and Legendre polynomials.
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Umbral Calculus and the Frobenius-Euler Polynomials
Abstract and Applied Analysis, 2013 We study some properties of umbral calculus related to the Appell sequence. From those properties, we derive new and interesting identities of the Frobenius-Euler polynomials.
Dae San Kim, Taekyun Kim, Sang-Hun Lee
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Sheffer and Non-Sheffer Polynomial Families
International Journal of Mathematics and Mathematical Sciences, 2012 By using the integral transform method, we introduce some non-Sheffer polynomial sets. Furthermore, we show how to compute the connection coefficients for particular expressions of Appell polynomials.
G. Dattoli +3 more
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Symbolic Methods Applied to a Class of Identities Involving Appell Polynomials and Stirling Numbers
MathematicsIn this paper, we present two symbolic methods, in particular, the method starting from the source identity, umbra identity, for constructing identities of s-Appell polynomials related to Stirling numbers and binomial coefficients.
Tian-Xiao He, Emanuele Munarini
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Certain Properties and Characterizations of Generalized Gould–Hopper-Based Hybrid Polynomials
MathematicsThis study offers a comprehensive generalization of the Gould–Hopper polynomials and their Appell-type analogs. Employing the quasi-monomiality approach, we delineate fundamental analytical characteristics, including recurrence relations, associated ...
Waseem Ahmad Khan +5 more
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Generalizations of the Bernoulli and Appell polynomials
Abstract and Applied Analysis, 2004 We first introduce a generalization of the Bernoulli polynomials, and consequently of the Bernoulli numbers, starting from suitable generating functions related to a class of Mittag-Leffler functions.
Gabriella Bretti +2 more
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A characterization of the Rogers q-hermite polynomials
International Journal of Mathematics and Mathematical Sciences, 1995 In this paper we characterize the Rogers q-Hermite polynomials as the only orthogonal polynomial set which is also 𝒟q-Appell where 𝒟q is the Askey-Wilson finite difference operator.
Waleed A. Al-Salam
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Approximation by operators including generalized Appell polynomials
Filomat, 2016 In this work, the problem of the approximation by certain poly- nomials is addressed. A new type operators sequence including generalized Appell polynomials are defi ned, qualitative and quantitative approximation theorems are proved. Some explicit examples of our operators involving Hermite polynomials of v variance, Gould-Hopper polynomials and ...
İÇÖZ, GÜRHAN +2 more
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AxiomsThis paper explores the operational principles and monomiality principles that significantly shape the development of various special polynomial families.
Awatif Muflih Alqahtani +3 more
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, 2021 In 1880, Paul Emile Appell introduced a certain kind of sequence which is named Appell polynomials in the literature. Besides the trivial examples, the most famous Appell polynomials are the Hermite, Bernoulli, and Euler polynomials. An interesting generalization of Appell polynomials, namely q-Appell polynomials were introduced by Walled A.
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