generalized Bernoulli polynomials
Congruences for Generalized Bernoulli Polynomials
... the generalized Bernoulli polynomials associated with a Dirichlet character χ are important in regard to sums of consecutive integers, all of which raised to the same ...
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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 [], ...
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On the Identities of Symmetry for the Generalized Bernoulli Polynomials Attached to of Higher Order
... Simsek, “On p-adic twisted q-L-functions related to generalized twisted Bernoulli numbers,” Russian Journal of Mathematical Physics, vol.. Kim, “New approach to the complete sum of produ[r] ...
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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 ...
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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 of ...
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K. Petr's Formula of Double Integral and Estimates of its Remainder
... numbers and polynomials , Adv. Ujevi´ c, On new estimation of the remainder in generalized Taylor’s formula , Math. Guo, Generalized Bernoulli polynomials , RGMIA Res. Guo, Darboux’s for[r] ...
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Relationships Between Generalized Bernoulli Numbers and Polynomials and Generalized Euler Numbers and Polynomials
... of Bernoulli and Euler numbers and polynomials In this section, we will restate definitions of (generalized) Bernoulli numbers, (generalized) Bernoulli polynomials, ...
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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 polynomials G ...
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Generalizations of Bernoulli numbers and polynomials
... of Bernoulli numbers B n , Bernoulli polynomials B n (x), and the gen- eralized Bernoulli numbers B n (a,b) are generalized to the one B n (x;a,b,c) which is called the ...
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A note on the Generalized Bernoulli and Euler Polynomials
... (ii) For non-integer m, there does not exist a random variable θ (m) such that e u −1 u m is the moment generating function of θ (m) . This follows, e.g., from the fact the uniform distribu- tion is not infinitely ...
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Bernoulli F polynomials and Fibo–Bernoulli matrices
... In this section, we define an interesting Fibo–Bernoulli matrix by using the Bernoulli F-polynomials. Then we obtain a factorization of the Fibo–Bernoulli matrix by using a generalized ...
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Bernoulli Basis and the Product of Several Bernoulli Polynomials
... Kim, “Some identities on the q-Euler polynomials of higher order and q-Stirling numbers by the fermionic p-adic integral on Zp ,” Russian Journal of Mathematical Physics, vol.. Simsek, “[r] ...
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q Bernoulli numbers and q Bernoulli polynomials revisited
... This paper performs a further investigation on the q -Bernoulli numbers and q - Bernoulli polynomials given by Acikgöz et al. (Adv Differ Equ, Article ID 951764, 9, 2010), some incorrect properties ...
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The Powers Sums, Bernoulli Numbers, Bernoulli Polynomials Rethinked
... the Bernoulli polynomials of order m under the form of diffe- rential operators acting on ...the Bernoulli poly- nomial of the same ...of Bernoulli polynomi- al multiplied with primitives of ...
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A New Approach to Bernoulli Numbers and Bernoulli Polynomials Related to Bernstein Polynomials
... q-Bernoulli polynomials. We give a new construction of these numbers and polynomials related to the second-kind Stirling numbers and q-Bernstein ...the generalized q- Bernoulli ...
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Hecke operators type and generalized Apostol-Bernoulli polynomials
... The Hecke operators have many applications in various spaces like the space of elliptic modular forms, the space of polynomials and others. Many mathematicians applied them to obtain applications in analytic ...
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Unified representation of the family of L functions
... The aim of this paper is to unify the family of L-functions. By using the generating functions of the Bernoulli, Euler and Genocchi polynomials, we construct unification of the L-functions. We also derive ...
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Barnes’ multiple Bernoulli and generalized Barnes’ multiple Frobenius Euler mixed type polynomials
... multiple Bernoulli polynomials as well as general- ized Barnes’ multiple Frobenius-Euler polynomials, we define and investigate the mixed- type polynomials of these ...these polynomials ...
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A Unification of the Generalized Multiparameter Apostol-type Bernoulli, Euler, Fubini, and Genocchi Polynomials of Higher Order
... or generalized Bernoulli, Euler, and Genocchi polyno- mials involve unifying any two or all of the three special types of polynomials (see, [1, 4, 9, 18, 19, 21, 24–26, 30, ...alized ...
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Identities on Genocchi Polynomials and Genocchi Numbers Concerning Binomial Coefficients
... Genocchi polynomials have a long ...Genocchi polynomials have become a popular research ...Genocchi polynomials extensively in many branches of Mathematics, such as elementary number theory, analytic ...
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