[PDF] Top 20 A note on the Generalized Bernoulli and Euler Polynomials
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A note on the Generalized Bernoulli and Euler Polynomials
... E i (m) ( x ) y n − i , (16) E n (m) ( x + 1 ) + E n (m) (x ) = 2E (m−1) n ( x ) . (17) In case m is an integer, let η j , i = 1 . . . m be an i.i.d sequence of random variables such that η j ∼ Ber( 1 / 2 ) . The Appell ... See full document
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A note on type 2 q Bernoulli and type 2 q Euler polynomials
... q-Euler polynomials. The type 2 q-Bernoulli polynomials and type 2 q-Euler polynomials are introduced respectively as the bosonic p-adic q-integrals on Z p ... 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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A Note on Symmetric Properties of the Twisted Bernoulli Polynomials and the Twisted Generalized Bernoulli Polynomials
... q-Bernoulli polynomials and the twisted generalized q-Bernoulli polynomi- als attached to χ of higher order and investigate some symmetric properties of ...q- Bernoulli numbers and ... See full document
13
Differential equations for the extended 2D Bernoulli and Euler polynomials
... these polynomials. Note that the above mentioned differential equations for the extended 2D Bernoulli polynomials reduce to the results obtained in (Bretti and Ricci in Taiwanese ... 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 Bernoulli polynomials B n (α) (x) of order α ∈ C , the generalized Euler polynomials E n (α) (x) of order α ∈ C and the generalized Genocchi ... See full document
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Relationships Between Generalized Bernoulli Numbers and Polynomials and Generalized Euler Numbers and Polynomials
... the Bernoulli and Euler polynomials are two classes of special ...about Bernoulli and Euler polynomials, for some examples, please refer to references in this ... See full document
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Probabilistic Proofs of Some Relationships Between the Bernoulli and Euler Polynomials
... In this section, we recall several probabilistic tools which will be needed in Section 3 for the probabilistic proofs of Theorems 1 and 2. First of all, Sun [12] gave the following probabilistic representation of the ... See full document
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Some New Classes of Generalized Apostol Euler and Apostol Genocchi Polynomials
... these polynomials have been ...the generalized Apostol-Bernoulli polynomials B α n x; λ of order α ∈ C; Luo 10 invented the generalized Apostol-Euler polynomials E α n x; ... See full document
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A note on Euler number and polynomials
... In [2], the authors proved the formulae of sums of products of Bernoulli numbers of higher order by using theory of residues. By using the properties of invariant p-adic integrals in this paper, we can also give ... See full document
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A Unification of the Generalized Multiparameter Apostol-type Bernoulli, Euler, Fubini, and Genocchi Polynomials of Higher Order
... and polynomials such as the Bernoulli numbers and polynomials, Euler numbers and polynomials, Genocchi numbers and polynomials, Fubini numbers and polynomials, and also ... See full document
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Barnes’ multiple Bernoulli and generalized Barnes’ multiple Frobenius Euler mixed type polynomials
... multiple Bernoulli polynomials as well as generalized Barnes’ multiple Frobenius-Euler polynomials, we define and investigate the mixed-type polynomials of these ...these ... See full document
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Unified representation of the family of L functions
... the generalized Bernoulli, Euler and Genocchi numbers and the generalized Bernoulli, Euler and Genocchi polynomials with parameters a, b, β and ...χ-extended ... See full document
10
Note on Nasybullin's Lemma Associated with the Modified Adic Euler Measure
... Kim, “A note on p-adic Euler measure on Zp ,” Russian Journal of Mathematical Physics, vol.. Carlitz, “q-Bernoulli numbers and polynomials,” Duke Mathematical Journal, vol.[r] ... See full document
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Identities on Genocchi Polynomials and Genocchi Numbers Concerning Binomial Coefficients
... numbers, Bernoulli numbers [14–16] and Euler numbers [14, ...Genocchi polynomials, the most common thing is to research on the relations between Genocchi polynomials, Bernoulli ... See full document
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On a class of generalized q Bernoulli and q Euler polynomials
... the generalized q-Bernoulli and q-Euler polynomials to obtain the main results of this paper in the next ...classical Bernoulli and Euler poly- ... See full document
10
New Taylor-like Expansions for Functions of Two Variables and Estimates of their Remainders
... Appell polynomials, Bernoulli polynomials, Euler polynomials, generalized Taylor’s formula, Taylor-like expansion, double integral, remainder.. The second author was supported in part by[r] ... See full document
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Viewing Some Ordinary Differential Equations from the Angle of Derivative Polynomials
... (the generalized) derivative polynomials, explicit formulas for the Bernoulli numbers and polynomials, for the Euler numbers and polynomials, for higher derivatives of some ... See full document
12
Recurrence formulae for Apostol Bernoulli and Apostol Euler polynomials
... for Bernoulli numbers to Apostol-Bernoulli and Apostol-Euler polynomials and ...classical Bernoulli and Euler polynomials and numbers stated in Nielsen’s classical book ... See full document
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Higher-order Euler-type polynomials and their applications
... higher-order Euler-type polynomials and ...a generalized partial Hecke operator and Euler-type polynomials and ...higher-order Euler-type polynomials is eigenfunctions for ... See full document
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