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[PDF] Top 20 On the Symmetric Properties for the Generalized Twisted Bernoulli Polynomials

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On the Symmetric Properties for the Generalized Twisted Bernoulli Polynomials

On the Symmetric Properties for the Generalized Twisted Bernoulli Polynomials

... the symmetric properties of the p-adic invariant integrals and investigated interesting relationships between the power sums and the Bernoulli polynomials see 2, 3, 6, 7, ... See full document

8

A Note on Symmetric Properties of the Twisted  Bernoulli Polynomials and the Twisted Generalized  Bernoulli Polynomials

A Note on Symmetric Properties of the Twisted Bernoulli Polynomials and the Twisted Generalized Bernoulli Polynomials

... the twisted q-Bernoulli polynomials and the twisted generalized q-Bernoulli polynomi- als attached to χ of higher order and investigate some symmetric properties of ... See full document

13

New approach to twisted q Bernoulli polynomials

New approach to twisted q Bernoulli polynomials

... constructed twisted Bernoulli polynomials together with twisted Bernoulli num- bers and obtained analytic properties of twisted L-functions [, ...the twisted ... See full document

21

On the Identities of Symmetry for the Generalized Bernoulli Polynomials Attached to  of Higher Order

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] ... 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

10. Some series identities for some special classes of Apostol-Bernoulli and Apostol-Euler polynomials related to generalized power and alternating sums

... interesting properties and relationships involving these polynomials [1, 2, 3, 4, 5, ...the generalized Apostol-Bernoulli polynomials B (α) n (x) of order α, 1991 Mathematics Subject ... See full document

15

Viewing Some Ordinary Differential Equations from the Angle of Derivative Polynomials

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 elementary ... See full document

12

Symmetric identities for Carlitz’s q Bernoulli numbers and polynomials

Symmetric identities for Carlitz’s q Bernoulli numbers and polynomials

... the twisted Lerch type Euler zeta ...on symmetric properties of the twisted q-Bernoulli polynomials and the twisted generalized q-Bernoulli ...Apostol-type ... See full document

10

Congruences for Generalized  Bernoulli Polynomials

Congruences for Generalized Bernoulli Polynomials

... further properties of p-adic q-L-function of two variables, which is recently constructed by Kim 2005 and Cenkci ...for generalized q-Bernoulli polynomials, which are q- extensions of the ... See full document

19

A note on the (h,q) zeta type function with weight α

A note on the (h,q) zeta type function with weight α

... interesting properties (see ...q-Bernstein polynomials and derived novel proper- ties of q-Bernoulli numbers with weight α by using the symmetric property of weighted q-Bernstein ... See full document

6

On Interpolation Functions of the Generalized Twisted  Euler Polynomials

On Interpolation Functions of the Generalized Twisted Euler Polynomials

... classical Bernoulli numbers negative ...p-adic twisted two-variable Euler-h, q-L-functions, which interpolate generalized twisted h, q- Euler polynomials at negative ... See full document

17

On the Symmetric Properties of the Multivariate  Adic Invariant Integral on  Associated with the Twisted Generalized Euler Polynomials of Higher Order

On the Symmetric Properties of the Multivariate Adic Invariant Integral on Associated with the Twisted Generalized Euler Polynomials of Higher Order

... Research Article On the Symmetric Properties of the Multivariate p-Adic Invariant Integral on Zp Associated with the Twisted Generalized Euler Polynomials of Higher Order Taekyun Kim,1 B[r] ... See full document

8

On the Symmetric Properties of Higher Order Twisted  Euler Numbers and Polynomials

On the Symmetric Properties of Higher Order Twisted Euler Numbers and Polynomials

... the twisted q-Euler numbers of order k. When k 1, the polynomials and numbers are called the twisted q-Euler polynomials and numbers, ...the polynomials and numbers are called the ... See full document

8

Some new identities on the twisted carlitz's q bernoulli numbers and q bernstein polynomials

Some new identities on the twisted carlitz's q bernoulli numbers and q bernstein polynomials

... and polynomials related to q-Bernstein ...these properties, we derive some new identities for the twisted q-Bernoulli numbers and ...the twisted Carlitz’s q-Bernoulli numbers and ... See full document

6

Hecke operators type and generalized Apostol-Bernoulli polynomials

Hecke operators type and generalized Apostol-Bernoulli polynomials

... of polynomials and ...other properties of the Hecke-eigenforms, which satisfy many interesting arithmetic ...Apostol-Bernoulli polynomials have been studied by many authors, for example, see ... See full document

11

Some New Classes of Generalized Apostol Euler and Apostol Genocchi Polynomials

Some New Classes of Generalized Apostol Euler and Apostol Genocchi Polynomials

... the generalized Apostol-Bernoulli polynomials B m−1,α n x, b, c; λ, m ∈ N, λ ∈ C, are defined, in a suitable neighborhood of t 0, with |t log b| < 2π if λ 1 or with |t log b| < | log λ| if λ / ... See full document

15

Singular values of three-parameter families $\lambda (\frac{e^{az}-1}{z})^{\mu}$ and $\lambda (\frac{z}{e^{az}-1})^{\eta}$

Singular values of three-parameter families $\lambda (\frac{e^{az}-1}{z})^{\mu}$ and $\lambda (\frac{z}{e^{az}-1})^{\eta}$

... dynamical properties of such functions. Some dynamical properties of families of such kinds of functions associated with exponential map are found in [5, 6, 8, 9, 10, ... See full document

8

On a class of generalized q Bernoulli and q Euler polynomials

On a class of generalized q Bernoulli and q Euler polynomials

... Carlitz firstly extended the classical Bernoulli and Euler numbers and polynomials, in- troducing them as q-Bernoulli and q-Euler numbers and polynomials [–]. There are nu- merous recent ... See full document

10

Higher-order Euler-type polynomials and their applications

Higher-order Euler-type polynomials and their applications

... Euler-type polynomials and ...a generalized partial Hecke operator and Euler-type polynomials and ...Euler-type polynomials is eigenfunctions for the generalized partial Hecke ...some ... See full document

11

New identities and relations derived from the generalized Bernoulli polynomials, Euler polynomials and Genocchi polynomials

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

9

Symmetry Properties of Higher Order Bernoulli Polynomials

Symmetry Properties of Higher Order Bernoulli Polynomials

... Hindawi Publishing Corporation Advances in Difference Equations Volume 2009, Article ID 318639, 6 pages doi 10 1155/2009/318639 Research Article Symmetry Properties of Higher Order Bernoulli Polynomia[.] ... See full document

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