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Lagrange-Based Hypergeometric Bernoulli Polynomials
Published 2022-05-01“…In this paper, we introduce the family of the Lagrange-based hypergeometric Bernoulli polynomials via the generating function method. …”
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Some Geometric Properties of a Family of Analytic Functions Involving a Generalized <i>q</i>-Operator
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Mixed-Type Hypergeometric Bernoulli–Gegenbauer Polynomials
Published 2023-09-01“…In this paper, we consider a novel family of the mixed-type hypergeometric Bernoulli–Gegenbauer polynomials. …”
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Discrete quasiprobability distributions involving Bernoulli polynomials
Published 2023-03-01“…The aim of this short paper is to present a new family of discrete densities with two parameters based on Bernoulli numbers and polynomials. …”
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Other approaches for generalized Bernoulli–Euler polynomials and beyond
Published 2023-06-01“…In this paper we develop two approaches for studying a large family of generalized Bernoulli–Euler polynomials. …”
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On Generalized Bivariate (<i>p</i>,<i>q</i>)-Bernoulli–Fibonacci Polynomials and Generalized Bivariate (<i>p</i>,<i>q</i>)-Bernoulli–Lucas Polynomials
Published 2023-04-01“…Finally, we provide some families of bilinear and bilateral generating functions for the generalized bivariate <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>p</mi><mo>,</mo><mi>q</mi><mo>)</mo></mrow></semantics></math></inline-formula>-Bernoulli–Fibonacci polynomials.…”
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A Family of Generalized Legendre-Based Apostol-Type Polynomials
Published 2022-01-01“…The purpose of this work is to provide a unified family of Legendre-based generalized Apostol-Bernoulli, Apostol-Euler, and Apostol-Genocchi polynomials, with appropriate constraints for the Maclaurin series. …”
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Primary resonance of an Euler-Bernoulli nano-beam modelled with second strain gradient
Published 2019-01-01“…<span style="font-family: 'Times New Roman','serif'; font-size: 10pt; mso-fareast-font-family: 'Times New Roman'; mso-ansi-language: EN-US; mso-fareast-language: EN-US; mso-bidi-language: AR-SA; mso-bidi-font-size: 9.0pt;">In the present manuscript, the second strain gradient (SSG) is utilized to investigate the primary resonance of a nonlinear Euler-Bernoulli nanobeam is analyzed in this paper for the first time. …”
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Some New Families of Special Polynomials and Numbers Associated with Finite Operators
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Comparison of Poisson and Bernoulli spatial cluster analyses of pediatric injuries in a fire district
Published 2008-09-01“…There was some overlap in geographic clusters identified by both methods. The Bernoulli method allows more focused cluster mapping and evaluation since it directly uses location data. …”
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New families of soliton solutions for the (2 + 1)-dimensional nonlinear evolution equation arising in nonlinear optics
Published 2023-04-01“…This article aims to achieve families of new traveling wave solutions to the (2 + 1)-dimensional nonlinear evolution equation using three powerful analytical techniques: the general form of Kudryashov’s method, the Bernoulli sub-ODE method, and the extended direct algebraic method. …”
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New Families of Special Polynomial Identities Based upon Combinatorial Sums Related to <i>p</i>-Adic Integrals
Published 2021-08-01“…Using these generating functions with their functional equation, we derive various interesting combinatorial sums and identities including new families of numbers and polynomials, the Bernoulli numbers, the Euler numbers, the Stirling numbers, the Daehee numbers, the Changhee numbers, and other numbers and polynomials. …”
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Using Fractional Bernoulli Wavelets for Solving Fractional Diffusion Wave Equations with Initial and Boundary Conditions
Published 2021-11-01“…In this paper, fractional-order Bernoulli wavelets based on the Bernoulli polynomials are constructed and applied to evaluate the numerical solution of the general form of Caputo fractional order diffusion wave equations. …”
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A New Class of Higher-Order Hypergeometric Bernoulli Polynomials Associated with Lagrange–Hermite Polynomials
Published 2021-04-01“…The purpose of this paper is to construct a unified generating function involving the families of the higher-order hypergeometric Bernoulli polynomials and Lagrange–Hermite polynomials. …”
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On parametric types of Apostol Bernoulli-Fibonacci, Apostol Euler-Fibonacci, and Apostol Genocchi-Fibonacci polynomials via Golden calculus
Published 2023-02-01“…This paper aims to give generating functions for the new family of polynomials, which are called parametric types of the Apostol Bernoulli-Fibonacci, the Apostol Euler-Fibonacci, and the Apostol Genocchi-Fibonacci polynomials by using Golden calculus. …”
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Identities and recurrence relations of special numbers and polynomials of higher order by analysis of their generating functions
Published 2018-08-01“…Relations between these new families of special numbers and polynomials and Bernoulli numbers and polynomials are given. …”
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