[PDF] Top 20 Relationships Between Generalized Bernoulli Numbers and Polynomials and Generalized Euler Numbers and Polynomials
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Relationships Between Generalized Bernoulli Numbers and Polynomials and Generalized Euler Numbers and Polynomials
... the generalized Bernoulli and Euler numbers and polynomials, and then discuss the relationships between the generalized Bernoulli and Euler ... See full document
8
Unified (p, q) -analog of Apostol type polynomials of order a
... type polynomials of order ...recurrence relationships, integral representations and so ...the generalized (p; q)-Stirling numbers of the second kind of order v, a correlation between ... See full document
10
New Taylor-like Expansions for Functions of Two Variables and Estimates of their Remainders
... Appell polynomials, Bernoulli polynomials, Euler polynomials, generalized Taylor’s formula, Taylor-like expansion, double integral, remainder.. The second author was supported in part by[r] ... See full document
14
Some Identities on the Generalized Bernoulli Numbers and Polynomials Associated with Volkenborn Integrals
... see 13. Recently, many authors have studied in the different several areas related to q- theory see 1–13. In this paper, we present a systemic study of some families of multiple Carlitz’s type q-Bernoulli ... See full document
17
Generalized Euler Numbers and Polynomials of Higher Order and Some Theoretic Identities
... q-Euler numbers and polynomials of higher order attached to Dirichlet’s character ...involving generalized q-Euler numbers and polynomials of higher ... See full document
6
Some results for the q Bernoulli, q Euler numbers and polynomials
... The q -analogues of many well known formulas are derived by using several results of q -Bernoulli, q -Euler numbers and polynomials. The q -analogues of ζ-type functions are given by using ... See full document
16
On a class of generalized q Bernoulli and q Euler polynomials
... classical Bernoulli and Euler numbers and polynomials, in- troducing them as q-Bernoulli and q-Euler numbers and polynomials ... See full document
10
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
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 ... See full document
8
SOME COMPUTATIONS BETWEEN SUMS OF POWERS OF CONSECUTIVE INTEGERS AND ALTERNATING SUMS OF POWERS OF CONSECUTIVE INTEGERS
... time, Bernoulli, Euler and Genocchi polynomials and numbers and its generalizations have been extensively studied and investigated by many mathematicians and physicists (see ...Genocchi ... See full document
6
A NOTE ON TYPE 2 DEGENERATE MULTI-POLY-BERNOULLI POLYNOMIALS AND NUMBERS
... the Bernoulli, Stirling and Eulerian numbers in ...many polynomials, theorems, numbers ...various numbers and ...Hermite polynomials in [3], the degenerate ... See full document
8
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 ... See full document
15
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. ... See full document
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Integral Formulae of Bernoulli and Genocchi Polynomials
... Kim, “Identities for the Bernoulli, the Euler and the Genocchi numbers and polynomials,” Advanced Studies in Contemporary Mathematics, vol.. Kim, “Integral formulae of Bernoulli polynomi[r] ... See full document
9
Several closed expressions for the Euler numbers
... the Bernoulli numbers, the Genocchi numbers, the tangent numbers, the Euler polynomials, the Stirling numbers of two kinds, and the Riemann zeta function, in number theory ... See full document
8
Singular values of three-parameter families $\lambda (\frac{e^{az}-1}{z})^{\mu}$ and $\lambda (\frac{z}{e^{az}-1})^{\eta}$
... Sajid, Singular values and fixed points of family of generating function of Bernoulli numbers, J. Yang, Several identities for the generalized Apostol-Bernoulli polynomials, Comput.[r] ... See full document
8
Some Relationships between the Analogs of Euler Numbers and Polynomials
... q-Euler numbers and ...q-Euler numbers and gener- alized twisted q-Euler numbers, ...of Euler numbers, which is ... See full document
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... Fubini numbers and polynomials by combining the q-Hermite polynomials and q- Fubini ...these numbers and polynomi- als, we derive some alternative summation formulas including powers of ... 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
... of generalized Apostol-Bernoulli and Apostol-Euler poly- nomials introduced lately by Srivastava et ...the generalized alternating sum and the analogues of the expansions of the hyperbolic ... See full document
15
Higher-order Euler-type polynomials and their applications
... higher-order Euler-type polynomials and ...a generalized partial Hecke operator and Euler-type polynomials and ...higher-order Euler-type polynomials is eigenfunctions for ... See full document
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