[PDF] Top 20 Some identities of higher order Barnes type q Bernoulli polynomials and higher order Barnes type q Euler polynomials
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Some identities of higher order Barnes type q Bernoulli polynomials and higher order Barnes type q Euler polynomials
... Some identities of higher order Barnes type q Bernoulli polynomials and higher order Barnes type q Euler polynomials Jang et al Advances in Difference Equations (2015) 2015 162 DOI 10 1186/s13662 015[.] ... See full document
8
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 q Extensions of Euler Numbers and Polynomials of Higher Order
... h, q-extension of Euler polynomials and numbers, see 14, ...new q-extension of Euler numbers and polynomials to be different which is treated by Ozden et ...our ... See full document
9
Some Identities on the 𝑞 Genocchi Polynomials of Higher Order and 𝑞 Stirling Numbers by the Fermionic 𝑝 Adic Integral on ℤ𝑝
... of some families of q-Genocchi numbers and families of polynomials of N ¨orlund type is presented by using the multivariate fermionic p-adic integral on ...these higher-order ... See full document
14
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
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
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
Barnes’ multiple Frobenius Euler and poly Bernoulli mixed type polynomials
... is a vector space isomorphism from P ∗ onto F . Henceforth, F denotes both the algebra of formal power series in t and the vector space of all linear functionals on P , and so an element f (t) of F will be thought of as ... See full document
16
Higher order Frobenius Euler and poly Bernoulli mixed type polynomials
... Henceforth, F will denote both the algebra of formal power series in t and the vector space of all linear functionals on P, and so an element f (t) of F will be thought of as both a formal power series and a linear ... See full document
13
A note on the Barnes type q Euler polynomials
... the Barnes-type q-Euler polynomials which are derived from the fermionic p-adic q-integrals and investigate some identities of these ...the ... See full document
7
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
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
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 ...derive some new interesting identities related to the Stirling numbers of the first kind and of the ... See full document
9
On Multiple Interpolation Functions of the Genocchi Polynomials
... the q-analogue of the Genocchi numbers and polynomials, recently, have been studied by many ...p-adic q-Vokenborn integral 6, Kim 2, 7–9, 14–18 constructed many kind of generating functions of the ... See full document
13
Some identities of higher order Bernoulli, Euler, and Hermite polynomials arising from umbral calculus
... derive some interesting identities of the higher-order Bernoulli, Euler, and Hermite polynomials arising from umbral calculus to have alternative ... See full document
10
Some Identities Related with the Higher-order Deformed Degenerate Bernoulli and Euler Polynomials
... the higher-order degenerate Bernoulli and Euler polynomials which were defined by Carlitz and define the higher-order deformed degenerate Bernoulli and Euler ... See full document
5
Barnes’ multiple Bernoulli and generalized Barnes’ multiple Frobenius Euler mixed type polynomials
... element f (t) of F will be thought of as both a formal power series and a linear functional. We call F umbral algebra, and umbral calculus is the study of umbral algebra. The order O(f (t)) of a power series f (t) ... See full document
16
Some identities on the higher order twisted q Euler numbers and polynomials with weight α
... of some families of higher- order-twisted q-Euler numbers and polynomials with weight a ...investigate higher-order-twisted q-Euler numbers and ... See full document
10
On a class of q Bernoulli and q Euler polynomials
... obtain some results for the above newly defined q-Bernoulli and q-Euler ...that q-Bernoulli and q-Euler polynomials in our definitions are ... See full document
11
Some results for the q Bernoulli, q Euler numbers and polynomials
... derive q-analogues of many well known formulas by using several results of q-Bernoulli, q-Euler numbers, and ...of q-Bernoulli, q-Euler numbers, and ... See full document
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