[PDF] Top 20 Some new identities of Frobenius Euler numbers and polynomials

... give some new and interesting identities which are derived from the basis of ...studied some identities of Frobenius-Euler ...interesting identities of ... See full document

... Kim, “A note on Bernstein polynomials associated with q-Euler numbers and polynomials,” International Journal of Mathematics and Analysis, vol... International Journal of Mathematics and[r] ... See full document

... type Frobenius-Euler numbers and polyno- mials and rthen develop some basic identities and ...establish some useful and interesting relations and formulas for the mentioned ... See full document

... study some properties of degenerate Changhee-Genocchi numbers and polynomials and give some new identities of these polynomials and numbers which are derived from ... See full document

... Bernoulli numbers and the classical Euler numbers, ...classical Euler polynomials. In fact, the classical Bernoulli polynomials can also be expressed by the classical ... See full document

... -Euler numbers and polynomials which are a slightly different Kim’s weighted q -Euler numbers and polynomials(see ...q-Euler numbers and polynomials, 2011]). ... See full document

... But we should notice that (2.5) and (2.6) are equivalent to (2.1) and (2.2), respectively. This is because when k goes from 0 to n, n −k also goes from 0 to k. Hence if we replace k by n −k in (2.1) and (2.2), we can ... See full document

... of some values of Euler ...studied some identities on Euler numbers and polynomials, and those on degenerate Euler numbers and polynomials, which are ... See full document

... Bernoulli numbers and the Euler numbers, ...the Frobenius-Euler polynomials give the Euler polynomials when λ = – in ...Bernoulli polynomials can be ... See full document

... introduce 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 ... See full document

... a new approach to the q-Euler numbers and polynomials of higher order attached to Dirichlet’s character ...derive some theoretic identities involving generalized q-Euler ... See full document

... the new type of degenerate poly- Bernoulli polynomials by means of the degenerate polylogarithm ...poly-Frobenius-Euler polynomials, called the new type of degenerate ... See full document

... the Frobenius-Euler polynomials. Some new formulae of products of the Frobenius-Euler polynomials are established by applying the generating function methods and ... See full document

... of some families of higher- order-twisted q-Euler numbers and polynomials with weight a ...q-Euler numbers and polynomials with weight a and establish interest- ing ... See full document

... a new construction of the q-extensions of Euler numbers and ...present new generating functions which are related to the q-Euler numbers and ...q-Euler polynomials ... See full document

... Kim and Kim Advances in Difference Equations 2012, 2012 196 http //www advancesindifferenceequations com/content/2012/1/196 R ES EA RCH Open Access Some identities of Frobenius Euler polynomials arisi[.] ... See full document

... We can write easily that [n] p,q = p n−1 [n] q/p , where [n] q/p is the q-number in q-calculus given by [n] q/p = (q/p) (q/p)−1 n −1 . Thereby, this implies that (p, q)-numbers and q-numbers are different, ... See full document

... view some ordinary differential equations and their solutions from the angle of (the generalized) derivative polynomials and simplify some known identities for the Bernoulli numbers and ... See full document

... polynomial identities in ...certain polynomials as linear combinations of that basis and hence to get some new and interesting polynomial ... See full document

... the introduction of degenerate gamma functions and degenerate Laplace transforms (see [7]). These already demonstrate that studying various degenerate versions of known spe- cial numbers and polynomials can ... See full document