[PDF] Top 20 Note on q Extensions of Euler Numbers and Polynomials of Higher Order
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Note on q Extensions of Euler Numbers and Polynomials of Higher Order
... and Euler numbers and polynomials are studied by many authors see for detail ...of higher-order twisted h, q-extension of Euler polynomials and numbers, by ... See full document
9
A Note on Genocchi Polynomials and Numbers of Higher Order
... studied q-Genocchi and Euler numbers using Fermionic q-integral and introduced related ...the q-extensions of the Euler numbers which can be viewed as interpolating ... See full document
6
Generalized Euler Numbers and Polynomials of Higher Order and Some Theoretic Identities
... to q-Euler numbers and polynomials of higher order attached to ...the q-Euler polynomials attached to χ, and have some identities involving these ... See full document
6
Note on the Extension of Barnes' Type Multiple Euler Polynomials
... the q-Euler numbers and polynomials of higher order, which are related to Barnes’ type multiple Euler numbers and ...our q-Euler polynomials of ... See full document
8
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] ... See full document
13
Apostol Type (p, q)-Frobenius-Euler Polynomials and Numbers
... (p, q)-extensions of Carlitz’s result ...(p, q)-Frobenius-Euler polynomials of order α and Apostol type (p, q)-Bernoulli ... See full document
14
On the Distribution of the Euler Polynomials and the Genocchi Polynomials of Higher Order
... extended higher order q-Euler and q-Genocchi ...the q-extension of the Apostol-Euler polynomials of order n, and the multiple Hurwitz zeta functions see ... See full document
9
Remarks on Sum of Products of Twisted Euler Polynomials and Numbers
... Carlitz’s q-Bernoulli number of higher order using an integral by the q-analogue μ q of the ordinary p-adic invariant ...of higher order q-Bernoulli ...Bernoulli ... See full document
8
Interpolation Functions of Extensions of Apostol's Type Euler Polynomials
... Apostol-Bernoulli polynomials, the Apostol-Euler polynomials, and their q-extensions ...some q-extensions of the Apostol-Bernoulli and the Apostol-Euler ... See full document
12
Arithmetic Identities Involving Bernoulli and Euler Numbers
... 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.. Kim, “Sym[r] ... See full document
11
Some Identities on the Twisted (ℎ,𝑞) Genocchi Numbers and Polynomials Associated with 𝑞 Bernstein 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.. Kim, “Sym[r] ... See full document
9
A note on the Barnes type q Euler polynomials
... the q-Euler polynomi- als of higher order and gave some interesting identities involving these ...of q-Bernoulli, q-Euler, and Bernstein polynomials (see [–, , ... See full document
7
A Note on Nörlund Type Twisted Euler Polynomials and Numbers of Higher Order Associated with Fermionic Invariant Integrals
... 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.. Kim, “Not[r] ... See full document
12
On the Twisted Analogs of the Generalized Euler Numbers and Polynomials of Higher Order
... Hindawi Publishing Corporation Advances in Difference Equations Volume 2010, Article ID 875098, 11 pages doi 10 1155/2010/875098 Research Article On the Twisted q Analogs of the Generalized Euler Numb[.] ... See full document
11
On the Symmetric Properties of Higher Order Twisted Euler Numbers and Polynomials
... twisted Euler polynomials of higher- order, ...the higher-order twisted q-Euler numbers and ...concerning higher- order twisted ... See full document
8
On a q analog of some numbers and polynomials
... new q-analogs of the Changhee numbers and polynomials of the first kind and of the second ...Stirling numbers of the first kind and of the second kind, the Euler polynomials of ... See full document
9
Some identities on the higher order twisted q Euler numbers and polynomials with weight α
... of higher- order-twisted q-Euler numbers and polynomials with weight a ...investigate higher-order-twisted q-Euler numbers and ... See full document
10
10. Some series identities for some special classes of Apostol-Bernoulli and Apostol-Euler polynomials related to generalized power and alternating sums
... (1.9) If we take a = 1, b = c = e in (1.7), (1.8) and (1.9) respectively, we have (1.4), (1.5) and (1.6). Obviously, when we set λ = 1, α = 1, a = 1, b = c = e in (1.7), (1.8) and (1.9), we have classical Bernoulli ... See full document
15
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... of q-Hermite- Fubini numbers and polynomials by combining the q-Hermite polynomials and q- Fubini ...these numbers and polynomi- als, we derive some alternative summation ... See full document
10
Some identities on the weighted q Euler numbers and q Bernstein polynomials
... weighted q -Euler numbers and polynomials which are a slightly different Kim’s weighted q -Euler numbers and polynomials(see ...A note on the weighted ... See full document
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