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Journal of Nonlinear Mathematical Physics Volume 13, 2006 - Issue 1
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Letters To The Editor

A Note on q−Bernoulli Numbers and Polynomials

A S Hegazi Mansoura University, 35516, Mansoura, Egypt E-mail: [email protected]
&
M Mansour Mansoura University, 35516, Mansoura, Egypt E-mail: [email protected]
Pages 9-18 | Received 17 May 2005, Accepted 15 Aug 2005, Published online: 21 Jan 2013

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Taekyun Kim. (2008) Symmetry p-adic invariant integral on ℤ for Bernoulli and Euler polynomials. Journal of Difference Equations and Applications 14:12, pages 1267-1277.
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Taekyun Kim, Daeyeoul Kim & Ja Kyung Koo. (2007) p-adic interpolating function associated with Euler numbers. Journal of Nonlinear Mathematical Physics 14:2, pages 250-257.
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Articles from other publishers (19)

Taekyun Kim, Dae San Kim & Hye Kyung Kim. (2022) λ - q -Sheffer sequence and its applications . Demonstratio Mathematica 55:1, pages 843-865.
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Semra Kuş, Naim Tuglu & Taekyun Kim. (2019) Bernoulli F-polynomials and Fibo–Bernoulli matrices. Advances in Difference Equations 2019:1.
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Alejandro Urieles, María José Ortega, William Ramírez & Samuel Vega. (2019) New results on the q -generalized Bernoulli polynomials of level m . Demonstratio Mathematica 52:1, pages 511-522.
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Hédi Elmonser. (2017) Symmetric q-Bernoulli numbers and polynomials. Functiones et Approximatio Commentarii Mathematici 56:2.
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M. Momenzadeh & I. Y. Kakangi. (2017) Approximation Properties of -Bernoulli Polynomials . Abstract and Applied Analysis 2017, pages 1-6.
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Dae San Kim & Taekyun Kim. (2014) Some identities of q-Euler polynomials arising from q-umbral calculus. Journal of Inequalities and Applications 2014:1.
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Dae San Kim & Tae Kyun Kim. (2014) q-Bernoulli polynomials and q-umbral calculus. Science China Mathematics 57:9, pages 1867-1874.
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Daeyeoul Kim, Ja Kyung Koo & Yoon Kyung Park. (2013) New approach to twisted q-Bernoulli polynomials. Advances in Difference Equations 2013:1.
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Lee-Chae Jang. (2012) Some identities on the twisted q-Bernoulli numbers and polynomials with weight α. Journal of Inequalities and Applications 2012:1.
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T. Kim, D. V. Dolgy, S. H. Lee, B. Lee & S. H. Rim. (2011) A Note on the Modified -Bernoulli Numbers and Polynomials with Weight . Abstract and Applied Analysis 2011, pages 1-8.
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T Kim, A Bayad & Y-H Kim. (2011) A Study on the -Adic -Integral Representation on Associated with the Weighted -Bernstein and -Bernoulli Polynomials. Journal of Inequalities and Applications 2011:1, pages 513821.
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Taekyun Kim, Seog-Hoon Rim & Byungje Lee. (2009) Some Identities of Symmetry for the Generalized Bernoulli Numbers and Polynomials. Abstract and Applied Analysis 2009, pages 1-8.
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Taekyun Kim & Young-Hee Kim. (2009) On the Symmetric Properties for the Generalized Twisted Bernoulli Polynomials. Journal of Inequalities and Applications 2009:1, pages 164743.
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T. Kim. (2008) q-Bernoulli numbers and polynomials associated with Gaussian binomial coefficients. Russian Journal of Mathematical Physics 15:1, pages 51-57.
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Taekyun Kim. (2008) q-Bernoulli Numbers Associated with q-Stirling Numbers. Advances in Difference Equations 2008, pages 1-11.
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Taekyun Kim. (2008) Euler Numbers and Polynomials Associated with Zeta Functions. Abstract and Applied Analysis 2008, pages 1-11.
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Taekyun Kim & Seog-Hoon Rim. (2007) New Changhee -Euler numbers and polynomials associated with -adic -integrals . Computers & Mathematics with Applications 54:4, pages 484-489.
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C. S. Ryoo. (2007) A numerical investigation of the structure of the roots ofq-Bernoulli polynomials. Journal of Applied Mathematics and Computing 23:1-2, pages 205-214.
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T. Kim. (2006) q-Generalized Euler numbers and polynomials. Russian Journal of Mathematical Physics 13:3, pages 293-298.
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