[PDF] Top 20 Some New Classes of Generalized Apostol Euler and Apostol Genocchi Polynomials
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Some New Classes of Generalized Apostol Euler and Apostol Genocchi Polynomials
... The generalized Bernoulli polynomials B n α x of order α ∈ C, the generalized Euler poly- nomials E α n x of order α ∈ C, and the generalized Genocchi polynomials G α n x ... See full document
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10. Some series identities for some special classes of Apostol-Bernoulli and Apostol-Euler polynomials related to generalized power and alternating sums
... The generalized Apostol-Bernoulli polynomials B (α) n (x; λ) of order α ∈ C , the generalized Apostol-Euler polynomials E (α) n (x; λ) of order α ∈ C , the ... See full document
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An extension of generalized Apostol Euler polynomials
... alized Apostol-Bernoulli polynomials and/or the generalized Apostol-Genocchi polyno- mials, only the nonnegative integer orders of these polynomials are considered and used ... See full document
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Some new formulas for the products of the Apostol type polynomials
... of new sums of the products of an arbitrary number of the classical Bernoulli and Euler polynomials by using the Euler basis for the vector space of polynomials of bounded ...establish ... See full document
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On the generalized Apostol type Frobenius Euler polynomials
... derive some new identities related to the Frobenius-Euler ...the generalized Frobenius-Euler polynomials and the generalized Hurwitz-Lerch zeta function at negative ... See full document
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Hermite based unified Apostol Bernoulli, Euler and Genocchi polynomials
... Hermite-based Apostol-Bernoulli, Euler and Genocchi ...obtain some symmetry identities between these polynomials and the generalized sum of integer ... See full document
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... als, Euler polynomials and Genocchi polynomials and obtained the (p, q)-analogues of familiar earlier formulas and ...a new generalization of Beta functions based on (p, q)-numbers and ... See full document
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New recurrence formulae for the Apostol Bernoulli and Apostol Euler polynomials
... of some connections between the classical Bernoulli numbers and the Stirling numbers of the second kind to establish a quadratic re- currence formula on the classical Bernoulli numbers, which was ... See full document
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New Extension of Unified Family Apostol Type of Polynomials and Numbers
... the new unified family of generalized Apos- tol-Bernoulli, Euler and Genocchi polynomials (see [9]) and generalized Stirling numbers of first kind (see ... See full document
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New identities and relations derived from the generalized Bernoulli polynomials, Euler polynomials and Genocchi polynomials
... Carlitz first extended the classical Bernoulli polynomials and numbers, Euler polynomi- als and numbers []. There are numerous recent investigations on this subject by many au- thors. Cheon [], Kurt [], ... See full document
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On the Distribution of the Euler Polynomials and the Genocchi Polynomials of Higher Order
... the Apostol-Euler polynomials of order n, and the multiple Hurwitz zeta functions see ...not new see 18, 20 and the definition of the Apostol-Bernoulli numbers in their paper are ... See full document
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Unified (p, q) -analog of Apostol type polynomials of order a
... of Apostol type polynomials of order . We have also analyzed some properties of them including addition property, derivative properties, recurrence relationships, integral representations and so ... See full document
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Some results for Apostol type polynomials associated with umbral algebra
... the Apostol-type polynomials was introduced and investigated recently by Luo and Srivastava (see ...of polynomials in a single variable x over all linear functional on ...obtain some ... See full document
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Reduction and duality of the generalized Hurwitz-Lerch zetas
... The paper can be summarized as follows. In Section , we state our main results. The Section contains the proofs of these results. In Section , by means of the main results, we get reduction and its dual formulas for ... See full document
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SOME COMPUTATIONS BETWEEN SUMS OF POWERS OF CONSECUTIVE INTEGERS AND ALTERNATING SUMS OF POWERS OF CONSECUTIVE INTEGERS
... Bernoulli, Euler and Genocchi polynomials and numbers and its generalizations have been extensively studied and investigated by many mathematicians and physicists (see ...two Genocchi ... See full document
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Some unified formulas and representations for the Apostol type polynomials
... the Apostol-type polynomials was introduced by Luo and Srivastava ...the Apostol-type polynomials and obtain their unified multiplication formula and explicit representations in terms of the ... See full document
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Some symmetry identities for the Apostol type polynomials related to multiple alternating sums
... 14:1267-1277, 2008; Abstr. Appl. Anal. 2008, doi:11.1155/2008/914347, Yang et al. in Discrete Math. 308:550-554, 2008; J. Math. Res. Expo. 30:457-464, 2010). Luo (Integral Transforms Spec. Funct. 20:377-391, 2009), ... See full document
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Singular values of three-parameter families $\lambda (\frac{e^{az}-1}{z})^{\mu}$ and $\lambda (\frac{z}{e^{az}-1})^{\eta}$
... which have more than one or infinitely many singular values. Often it is crucial to investigate the dynamical properties of such functions. Some dynamical properties of families of such kinds of functions ... See full document
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... q-Hermite polynomials are special or limiting case of the orthogonal poly- nomials as they contain no parameter other than q and appears to be at the bottom of a hierarchy of the classical polynomials ... See full document
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Construction of Fourier expansion of Apostol Frobenius–Euler polynomials and its applications
... Frobenius–Euler polynomials and their various generalizations such as the Apostol Frobenius–Euler polynomials have been studied intensively by some ...Frobenius–Euler ... See full document
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