bernoulli polynomials and numbers
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 ...
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q Bernoulli numbers and q Bernoulli polynomials revisited
... of Bernoulli numbers and polynomials, many mathematicians have studied q-Bernoulli numbers and q-Bernoulli polynomials (see ...q-Bernoulli numbers and ...
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A New Approach to Bernoulli Numbers and Bernoulli Polynomials Related to Bernstein Polynomials
... q-Bernoulli numbers and q-Bernoulli ...these numbers and polynomials related to the second-kind Stirling numbers and q-Bernstein ...q- Bernoulli polynomials ...
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The Powers Sums, Bernoulli Numbers, Bernoulli Polynomials Rethinked
... that Bernoulli polynomials of odd order vanish for arguments equal to 0, 1/2, 1, we obtain easily the Faulhaber formula for pow- ers sums in term of polynomials in λ having coefficients depending on ...
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Applications of q-Umbral Calculus to Modi ed Apostol Type q-Bernoulli Polynomials
... q-Bernoulli polynomials, q-Euler polynomials and various general- izations of these polynomials ...q-Bernoulli numbers and polynomials, and we apply these numbers ...
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A note on Carlitz q Bernoulli numbers and polynomials
... In Section 3, we construct the complex, analytic, two-variable q-L-function that is a q- analog of the two-variable L-function. Using this function, we calculate the values of two- variable q-L-functions at nonpositive ...
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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 ...
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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] ...
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Symmetric identities for Carlitz’s q Bernoulli numbers and polynomials
... q-Bernoulli numbers and q-Bernoulli polynomials is performed, and several symmetric identities for these numbers and polynomials are established by applying elementary methods ...
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Relationships Between Generalized Bernoulli Numbers and Polynomials and Generalized Euler Numbers and Polynomials
... of Bernoulli and Euler numbers and polynomials In this section, we will restate definitions of (generalized) Bernoulli numbers, (generalized) Bernoulli polynomials, ...
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Unified (p, q) -analog of Apostol type polynomials of order a
... of Bernoulli polynomials, Euler poly- nomials and Genocchi polynomials and acquired the (p; q)-analogues of known earlier ...Genocchi polynomials and derived their some ...for ...
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A note on degenerate Bernstein polynomials
... Bernstein polynomials, the degenerate Bernstein polynomi- als were introduced recently (see ...Bernstein polynomials some fundamental properties and identities associated with special numbers and ...
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Identities on Genocchi Polynomials and Genocchi Numbers Concerning Binomial Coefficients
... Genocchi numbers, the most common thing comes to our mind is to research the relations between Genocchi numbers, Bernoulli numbers [14–16] and Euler numbers [14, ...Genocchi ...
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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 ...
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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 ...
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Special Numbers on Analytic Functions
... factorial numbers T n k ( ) , on analytic func- ...factorial numbers T n k ( ) , , which are defined by means of the following generating function ...
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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 generating ...
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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
... Abstract. The purpose of this paper is to obtain several series identities in- volving some classes of generalized Apostol-Bernoulli and Apostol-Euler poly- nomials introduced lately by Srivastava et al. in [16, ...
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New results on higher order Daehee and Bernoulli numbers and polynomials
... Daehee numbers and polynomials, higher-order λ -Daehee numbers and polynomials, and twisted λ -Daehee numbers and polynomials of order ...Daehee numbers and ...these ...
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Higher-order Euler-type polynomials and their applications
... Euler-type polynomials and ...Euler-type polynomials and ...Euler-type polynomials is eigenfunctions for the generalized partial Hecke ...these polynomials and ...
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