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Some Remarks for the Relationships between the Generalized Bernoulli and Euler Polynomials 被引量:1
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作者 LUO Qiu-ming GE Shu-mei 《Chinese Quarterly Journal of Mathematics》 CSCD 2010年第1期16-22,共7页
In this paper,we prove the Srivastava-Pint'er's addition theorems(see Applied Mathematic Lett.17(2004),375-380) by applying the another methods.We also provide some analoges of these addition theorems and dedu... In this paper,we prove the Srivastava-Pint'er's addition theorems(see Applied Mathematic Lett.17(2004),375-380) by applying the another methods.We also provide some analoges of these addition theorems and deduce the corresponding special cases. 展开更多
关键词 Bernoulli polynomials and numbers euler polynomials and numbers generalized Bernoulli polynomials and numbers generalized euler polynomials and numbers generating functions Srivastava-Pinter's addition theorem
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A Note on Bell-Based Bernoulli and Euler Polynomials of Complex Variable
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作者 N.Alam W.A.Khan +5 位作者 S.Obeidat G.Muhiuddin N.S.Diab H.N.Zaidi A.Altaleb L.Bachioua 《Computer Modeling in Engineering & Sciences》 SCIE EI 2023年第4期187-209,共23页
In this article,we construct the generating functions for new families of special polynomials including two parametric kinds of Bell-based Bernoulli and Euler polynomials.Some fundamental properties of these functions... In this article,we construct the generating functions for new families of special polynomials including two parametric kinds of Bell-based Bernoulli and Euler polynomials.Some fundamental properties of these functions are given.By using these generating functions and some identities,relations among trigonometric functions and two parametric kinds of Bell-based Bernoulli and Euler polynomials,Stirling numbers are presented.Computational formulae for these polynomials are obtained.Applying a partial derivative operator to these generating functions,some derivative formulae and finite combinatorial sums involving the aforementioned polynomials and numbers are also obtained.In addition,some remarks and observations on these polynomials are given. 展开更多
关键词 Bernoulli polynomials euler polynomials bell polynomials stirling numbers
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Obtaining Simply Explicit Form and New Properties of Euler Polynomials by Differential Calculus
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作者 Do Tan Si 《Applied Mathematics》 2023年第7期460-480,共21页
Utilization of the shift operator to represent Euler polynomials as polynomials of Appell type leads directly to its algebraic properties, its relations with powers sums;may be all its relations with Bernoulli polynom... Utilization of the shift operator to represent Euler polynomials as polynomials of Appell type leads directly to its algebraic properties, its relations with powers sums;may be all its relations with Bernoulli polynomials, Bernoulli numbers;its recurrence formulae and a very simple formula for calculating simultaneously Euler numbers and Euler polynomials. The expansions of Euler polynomials into Fourier series are also obtained;the formulae for obtaining all π<sup>m</sup> as series on k<sup>-m</sup> and for expanding functions into series of Euler polynomials. 展开更多
关键词 Obtaining Appell Type euler Numbers and polynomials Relations euler-Bernoulli polynomials Sums over km Series on k-m euler Series of Functions
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Some Symmetry Identities for the Euler Polynomials
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作者 Sheng Liang YANG Zhan Ke QIAO 《Journal of Mathematical Research and Exposition》 CSCD 2010年第3期457-464,共8页
Using the generating functions, we prove some symmetry identities for the Euler polynomials and higher order Euler polynomials, which generalize the multiplication theorem for the Euler polynomials. Also we obtain som... Using the generating functions, we prove some symmetry identities for the Euler polynomials and higher order Euler polynomials, which generalize the multiplication theorem for the Euler polynomials. Also we obtain some relations between the Bernoulli polynomials, Euler polynomials, power sum, alternating sum and Genocchi numbers. 展开更多
关键词 euler polynomial Bernoulli number Bernoulli polynomial Genocchi number power sum alternating sum.
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On Polynomials Rn(x) Related to the Stirling Numbers and the Bell Polynomials Associated with the p-Adic Integral on
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作者 Hui Young Lee Cheon Seoung Ryoo 《Open Journal of Discrete Mathematics》 2016年第2期89-98,共10页
In this paper, one introduces the polynomials R<sub>n</sub>(x) and numbers R<sub>n</sub> and derives some interesting identities related to the numbers and polynomials: R<sub>n</sub>... In this paper, one introduces the polynomials R<sub>n</sub>(x) and numbers R<sub>n</sub> and derives some interesting identities related to the numbers and polynomials: R<sub>n</sub> and R<sub>n</sub>(x). We also give relation between the Stirling numbers, the Bell numbers, the R<sub>n</sub> and R<sub>n</sub>(x). 展开更多
关键词 The euler Numbers and polynomials The Stirling Numbers The Bell polynomials and Numbers
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