Bernoulli Numbers
q Bernoulli numbers and q Bernoulli polynomials revisited
... -Bernoulli numbers and q - Bernoulli polynomials given by Acikgöz et ...-Bernoulli numbers and polynomials is ...-Bernoulli numbers and polynomials are ...
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On modified degenerate Carlitz q Bernoulli numbers and polynomials
... 12. Kim, T: On the weighted q-Bernoulli numbers and polynomials. Adv. Stud. Contemp. Math. 21(2), 201-2015 (2011) 13. Kim, T, Kim, DS, Seo, J-J: Fully degenerate poly-Bernoulli numbers and ...
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A Double Inequality for the Ratio of Two Consecutive Bernoulli Numbers
... These numerical values hint us the approximating accuracy of the lower and up- per bounds in the double inequality (1.3) for the ratio of two consecutive Bernoulli numbers with even indexes: as k becomes ...
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Bernoulli numbers and certain convolution sums with divisor functions
... Kim et al Advances in Difference Equations 2013, 2013 277 http //www advancesindifferenceequations com/content/2013/1/277 R ES EA RCH Open Access Bernoulli numbers and certain convolution sums with di[.] ...
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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 and ...
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A note on poly Bernoulli numbers and polynomials of the second kind
... Kim et al Advances in Difference Equations 2014, 2014 219 http //www advancesindifferenceequations com/content/2014/1/219 R ES EARCH Open Access A note on poly Bernoulli numbers and polynomials of the[.] ...
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A note on degenerate poly Bernoulli numbers and polynomials
... A note on degenerate poly Bernoulli numbers and polynomials Kim and Kim Advances in Difference Equations (2015) 2015 258 DOI 10 1186/s13662 015 0595 3 R E S E A R C H Open Access A note on degenerate[.] ...
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Multiparameter Higher Order Daehee and Bernoulli Numbers and Polynomials
... and Bernoulli numbers and ...hee numbers and polynomials of the first and second ...these numbers and polynomials. The relations be- tween these numbers and Stirling and ...
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Some Identities of Bernoulli Numbers and Polynomials Associated with Bernstein Polynomials
... Hindawi Publishing Corporation Advances in Difference Equations Volume 2010, Article ID 305018, 7 pages doi 10 1155/2010/305018 Research Article Some Identities of Bernoulli Numbers and Polynomials As[.] ...
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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 numbers and ...
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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 ...
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Some identities on the twisted q Bernoulli numbers and polynomials with weight α
... By using the p-adic q-integral on Zp , we give some identities and relations on the twisted q-Bernoulli numbers and polynomials with weight α.... Jang Journal of Inequalities and Applica[r] ...
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Bernoulli numbers, convolution sums and congruences of coefficients for certain generating functions
... Abstract In this paper, we study the convolution sums involving restricted divisor functions, their generalizations, their relations to Bernoulli numbers, and some interesting applicatio[r] ...
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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, (generalized) Euler ...
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The Powers Sums, Bernoulli Numbers, Bernoulli Polynomials Rethinked
... of Bernoulli was proven in 1755 based on the calculus of finite difference by Euler [7], a researcher working with the Ber- noulli brothers at ...denomination Bernoulli numbers, introduced the ...
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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 generalized ...
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Several properties of hypergeometric Bernoulli numbers
... hypergeometric Bernoulli numbers, including several identities for hypergeometric Bernoulli numbers which the convergents of the continued fraction expansion of the generating function of the ...
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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 attached to ...
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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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Identities on Genocchi Polynomials and Genocchi Numbers Concerning Binomial Coefficients
... of numbers or the three kinds of ...Genocchi numbers themselves and Genocchi polynomials ...Genocchi numbers (polynomials), Bernoulli numbers (polynomials) and Euler numbers ...
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