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Generalized Bernoulli–Laguerre Polynomials: Applications in Coupled Nonlinear System of Variable-Order Fractional PDEs
In this paper, we introduce a general class of coupled nonlinear systems of variable-order fractional partial differential equations (GCNSV-FPDEs)...
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Characterization of the Bernoulli polynomials via the Raabe functional equation
The purpose of the present paper is to show that in certain classes of real (or complex) functions, Bernoulli polynomials are essentially the only...
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An efficient iterative method for multi-order nonlinear fractional differential equations based on the integrated Bernoulli polynomials
We present an effective practical approach for solving multi-order nonlinear fractional differential equations. Our method uses integrated Bernoulli...
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Generalized degenerate Bernoulli numbers and polynomials arising from Gauss hypergeometric function
A new family of p -Bernoulli numbers and polynomials was introduced by Rahmani (J. Number Theory 157:350–366,
2015 ) with the help of the Gauss... -
Continued fraction representation of the generating function of Bernoulli polynomials
Continued fraction and quasi-reciprocal continued fraction expansions of the generating function of Bernoulli numbers have been obtained. The...
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Certain properties of 3D degenerate generalized Fubini polynomials and applications
A renewed interest in combinatorial and arithmetic properties as well as applications to differential equations, identities, formulas, and...
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On the orthogonality of Atkin-like polynomials and orthogonal polynomial expansion of generalized Faber polynomials
In this paper, we consider the Atkin-like polynomials that appeared in the study of normalized extremal quasimodular forms of depth 1 on
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Unified Bernoulli-Euler polynomials of Apostol type
The object of this paper is to introduce and study the properties of unified Apostol-Bernoulli and Apostol-Euler polynomials noted by
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Bell based Apostol-Bernoulli polynomials and its properties
In this present paper, we define a generating function of mix type polynomials known as Bell based Apostol-Bernoulli polynomials of order
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Recurrence relations, associated formulas, and combinatorial sums for some parametrically generalized polynomials arising from an analysis of the Laplace transform and generating functions
The aim of this paper is to obtain some interesting infinite series representations for the Apostol-type parametrically generalized polynomials with...
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Some combinatorial identities of the degenerate Bernoulli and Euler-Genocchi polynomials
The main purpose of the present paper is to investigate some properties and combinatorial identities of the degenerate Bernoulli and Euler-Genocchi...
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Approximation by Haar and Walsh Polynomials in Weighted Generalized Grand Lebesgue Space
AbstractIn the paper we give direct theorems on approximation by Haar and Walsh polynomials in weighted generalized grand Lebesgue space. Also the...
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Novel formulas of moments of Negative Binomial distribution connected with Apostol-Bernoulli numbers of higher order and Stirling numbers
The main subject of this article is to present and reveal some new relationships between the moment generating functions of the Negative Binomial...
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Boole-Dunkl polynomials and generalizations
Appell sequences of polynomials can be extended to the Dunkl context replacing the ordinary derivative by the Dunkl operator on the real line, and...
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A kind of bivariate Bernoulli-type multiquadric quasi-interpolation operator with higher approximation order
In this paper, a kind of bivariate Bernoulli-type multiquadric quasi-interpolation operator is studied by combining the known multiquadric...
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A computational method based on the generalized Lucas polynomials for fractional optimal control problems
Nonorthogonal polynomials have many useful properties like being used as a basis for spectral methods, being generated in an easy way, having...
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A Note on Hermite-Bernoulli Polynomials
Using the concepts and formalism of different families of Hermite polynomials, we discuss here some generalizations of polynomials belonging to the...
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Generalized Bernoulli Numbers, Cotangent Power Sums, and Higher-Order Arctangent Numbers
We explore several interesting consequences of an explicit formula expressing cotangent power sums by generalized Bernoulli numbers. In particular,...