Bernoulli polynomials
Congruences for Generalized Bernoulli Polynomials
... q-Bernoulli polynomials, which are q- extensions of the classes for generalized Bernoulli numbers and polynomials given by Fox 2000, Gunaratne 1995, and Young 1999, ...
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q Bernoulli numbers and q Bernoulli polynomials revisited
... In this section, we perform a further investigation on the q-Bernoulli numbers and q- Bernoulli polynomials given by Acikgöz et al. [7], some incorrect properties are revised. Definition 1 (Acikgöz ...
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Some generalizations of 2D Bernoulli polynomials
... 2D Bernoulli polynomials, neo-Bernoulli polynomials are introduced from a point of view involving the use of nonexponential generating ...
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A note on higher order Bernoulli polynomials
... Kim and Kim Journal of Inequalities and Applications 2013, 2013:111 http://www.journalofinequalitiesandapplications.com/content/2013/1/111.. A note on higher-order Bernoulli polynomials D[r] ...
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On the Symmetric Properties for the Generalized Twisted Bernoulli Polynomials
... polynomials cf. 3, 6, 7, 13, 14, 20–27. The authors of this paper have established various identities by the symmetric properties of the p-adic invariant integrals and investigated interesting relationships ...
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On q analogs of degenerate Bernoulli polynomials
... degenerate Bernoulli polynomials were introduced by Carlitz and rediscovered later by Ustiniv under the name of Korobov polynomials of the second kind (see Carlitz in ...degenerate Bernoulli ...
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A new construction on the q Bernoulli polynomials
... -Bernoulli polynomials and numbers, then indicate the ambiguities on the Açikgöz et ...-Bernoulli polynomials and redefine ...-Bernoulli polynomials is ...
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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. Cheon [], Kurt [], ...
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New approach to twisted q Bernoulli polynomials
... the Bernoulli polynomials and Bernoulli numbers have gained considerable sig- nificance in the fields of physics and mathematics ...the Bernoulli polynomials and Bernoulli numbers, ...
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The Powers Sums, Bernoulli Numbers, Bernoulli Polynomials Rethinked
... the Bernoulli polynomials of order m under the form of diffe- rential operators acting on ...the Bernoulli poly- nomial of the same ...of Bernoulli polynomi- al multiplied with primitives of ...
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A NOTE ON TYPE 2 DEGENERATE MULTI-POLY-BERNOULLI POLYNOMIALS AND NUMBERS
... multi-poly-Genocchi polynomials given by using the degenerate multi-polyexponential ...multi-poly-Bernoulli polynomials, called the type 2 degenerate multi-poly-Bernoulli poly- nomials by ...
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Hecke operators type and generalized Apostol-Bernoulli polynomials
... The Hecke operators have many applications in various spaces like the space of elliptic modular forms, the space of polynomials and others. Many mathematicians applied them to obtain applications in analytic ...
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A New Approach to Bernoulli Numbers and Bernoulli Polynomials Related to Bernstein Polynomials
... q-Bernoulli polynomials. We give a new construction of these numbers and polynomials related to the second-kind Stirling numbers and q-Bernstein ...q- Bernoulli polynomials attached to ...
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A Note on Symmetric Properties of the Twisted Bernoulli Polynomials and the Twisted Generalized Bernoulli Polynomials
... q-Bernoulli polynomials and the twisted generalized q-Bernoulli polynomi- als attached to χ of higher order and investigate some symmetric properties of ...q- Bernoulli numbers and ...
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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] ...
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Symmetry Properties of Higher Order Bernoulli Polynomials
... Hindawi Publishing Corporation Advances in Difference Equations Volume 2009, Article ID 318639, 6 pages doi 10 1155/2009/318639 Research Article Symmetry Properties of Higher Order Bernoulli Polynomia[.] ...
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On a class of q Bernoulli and q Euler polynomials
... q-Bernstein polynomials and Phillips q-Bernoulli polynomials and derive the formulas involving the q-Stirling numbers of the second kind, q-Bernoulli polynomials and Phillips ...
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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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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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Download PDF
... and polynomials and give some properties of these numbers and ...and polynomials and some relationships between q-Bernoulli polynomials, q-Euler polynomials and q-Genocchi ...
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