Results 21 to 30 of about 1,405 (108)
On the q-Extension of Apostol-Euler Numbers and Polynomials [PDF]
Abstract and Applied Analysis, 2008 Recently, Choi et al. (2008) have studied the q‐extensions of the Apostol‐Bernoulli and the Apostol‐Euler polynomials of order n and multiple Hurwitz zeta function. In this paper, we define Apostol′s type q‐Euler numbers En,q,ξ and q‐Euler polynomials En,q,ξ(x). We obtain the generating functions of En,q,ξ and En,q,ξ(x), respectively.
Lee-Chae Jang, Wonjoo Kim, Young-Hee Kim
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Applications and Properties for Bivariate Bell‐Based Frobenius‐Type Eulerian Polynomials
Journal of Function Spaces, Volume 2023, Issue 1, 2023., 2023 In this study, we introduce sine and cosine Bell‐based Frobenius‐type Eulerian polynomials, and by presenting several relations and applications, we analyze certain properties. Our first step is to obtain diverse relations and formulas that cover summation formulas, addition formulas, relations with earlier polynomials in the literature, and ...
Waseem Ahmad Khan +3 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
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An extension of generalized Apostol-Euler polynomials [PDF]
Advances in Difference Equations, 2013 Abstract Recently, Tremblay, Gaboury and Fugère introduced a class of the generalized Bernoulli polynomials (see Tremblay in Appl. Math. Let. 24:1888-1893, 2011). In this paper, we introduce and investigate an extension of the generalized Apostol-Euler polynomials.
Chen, Si, Cai, Yi, Luo, Qiu-Ming
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Unification of Two‐Variable Family of Apostol‐Type Polynomials with Applications
Journal of Mathematics, Volume 2022, Issue 1, 2022., 2022 In this paper, the two‐variable unified family of generalized Apostol‐type polynomials is introduced, and some implicit forms and general symmetry identities are derived. Also, we obtain new degenerate Apostol‐type numbers and polynomials constructed from the new 2‐variable unified family.
Beih S. El-Desouky +3 more
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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
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Journal of Applied Mathematics, Volume 2021, Issue 1, 2021., 2021 Asymptotic approximations of Tangent polynomials, Tangent‐Bernoulli, and Tangent‐Genocchi polynomials are derived using saddle point method and the approximations are expressed in terms of hyperbolic functions. For each polynomial there are two approximations derived with one having enlarged region of validity.
Cristina B. Corcino +3 more
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Recurrence formulae for Apostol-Bernoulli and Apostol-Euler polynomials [PDF]
Advances in Difference Equations, 2012 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
He, Yuan, Wang, Chunping
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Asymptotic estimates for Apostol-Bernoulli and Apostol-Euler polynomials [PDF]
Mathematics of Computation, 2012 We analyze the asymptotic behavior of the Apostol-Bernoulli polynomials $\mathcal{B}_{n}(x; )$ in detail. The starting point is their Fourier series on $[0,1]$ which, it is shown, remains valid as an asymptotic expansion over compact subsets of the complex plane.
Navas, L.M., Ruiz, F.J., Varona, J.L.
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q-Apostol–Euler Polynomials and q-Alternating Sums [PDF]
Ukrainian Mathematical Journal, 2014 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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