Advanced search
Publication Cover
Journal of Difference Equations and Applications Volume 14, 2008 - Issue 12
Submit an article Journal homepage
163
Views
62
CrossRef citations to date
0
Altmetric
Original Articles

Symmetry p-adic invariant integral on ℤp for Bernoulli and Euler polynomials

Taekyun Kim EECS, Kyungpook National University, Taegu, 702-701, South KoreaCorrespondence[email protected]
Pages 1267-1277 | Received 08 Dec 2007, Accepted 24 Jan 2008, Published online: 20 Oct 2008

Citations (62)

Keep up to date with the latest research on this topic with citation updates for this article.

Subscribe to citation updates

Read on this site (4)

Waseem Ahmad Khan, Jihad Younis, Ugur Duran & Azhar Iqbal. (2022) The higher-order type 2 Daehee polynomials associated with p-adic integral on ℤ. Applied Mathematics in Science and Engineering 30:1, pages 573-582.
Read now
Dae San Kim & Taekyun Kim. (2014) A note on Boole polynomials. Integral Transforms and Special Functions 25:8, pages 627-633.
Read now
Yilmaz Simsek. (2010) Complete sum of products of (h, q)-extension of Euler polynomials and numbers. Journal of Difference Equations and Applications 16:11, pages 1331-1348.
Read now
Weiping Wang & Wenwen Wang. (2010) Some results on power sums and Apostol-type polynomials. Integral Transforms and Special Functions 21:4, pages 307-318.
Read now

Articles from other publishers (58)

Yuan He. (2023) Applications of Symmetric Identities for Apostol–Bernoulli and Apostol–Euler Functions. Symmetry 15:7, pages 1384.
Crossref
Abdelmejid Bayad & Yilmaz Simsek. (2021) Multiple Dedekind Type Sums and Their Related Zeta Functions. Mathematics 9:15, pages 1744.
Crossref
Taekyun Kim, Dae San Kim, Han Young Kim & Jongkyum Kwon. (2020) Identities of symmetry for Bernoulli polynomials and power sums. Journal of Inequalities and Applications 2020:1.
Crossref
Sang Jo Yun & Jin-Woo Park. (2020) On Fully Degenerate Daehee Numbers and Polynomials of the Second Kind. Journal of Mathematics 2020, pages 1-9.
Crossref
Dae San Kim & Taekyun Kim. (2019) Some applications of degenerate poly-Bernoulli numbers and polynomials. Georgian Mathematical Journal 26:3, pages 415-421.
Crossref
Joohee Jeong, Dong-Jin Kang & Seog-Hoon Rim. (2018) Symmetry Identities of Changhee Polynomials of Type Two. Symmetry 10:12, pages 740.
Crossref
SangKi Choi, Taekyun Kim, Hyuck-In Kwon & Jongkyum Kwon. (2018) Quadratic symmetry of modified q-Euler polynomials. Advances in Difference Equations 2018:1.
Crossref
Serkan Araci, Waseem Khan & Kottakkaran Nisar. (2018) Symmetric Identities of Hermite-Bernoulli Polynomials and Hermite-Bernoulli Numbers Attached to a Dirichlet Character χ. Symmetry 10:12, pages 675.
Crossref
Taekyun Kim & Dae San Kim. (2017) Identities of Symmetry for Degenerate Euler Polynomials and Alternating Generalized Falling Factorial Sums. Iranian Journal of Science and Technology, Transactions A: Science 41:4, pages 939-949.
Crossref
Feng Qi, Serkan Araci & Mehmet Acikgoz. (2017) On an Analogue of Euler Polynomials and Related to Extended Fermionic p-Adic Integrals on $$ {\mathbb{Z}}_{p} $$ Z p. Iranian Journal of Science and Technology, Transactions A: Science 41:3, pages 613-618.
Crossref
Dongkyu Lim & Younghae Do. (2015) Some identities of Barnes-type special polynomials. Advances in Difference Equations 2015:1.
Crossref
Yuan He, Serkan Araci, H.M. Srivastava & Mehmet Acikgoz. (2015) Some new identities for the Apostol–Bernoulli polynomials and the Apostol–Genocchi polynomials. Applied Mathematics and Computation 262, pages 31-41.
Crossref
Dmitry V. Dolgy, Dae San Kim, Taekyun Kim & Toufik Mansour. (2015) Barnes-type degenerate Euler polynomials. Applied Mathematics and Computation 261, pages 388-396.
Crossref
Dae San Kim, Taekyun Kim & Dmitry V. Dolgy. (2015) A note on degenerate Bernoulli numbers and polynomials associated with p-adic invariant integral on . Applied Mathematics and Computation 259, pages 198-204.
Crossref
Tae Kyun Kim. (2015) Barnes? type multiple degenerate Bernoulli and Euler polynomials. Applied Mathematics and Computation 258, pages 556-564.
Crossref
Dae San Kim. (2015) SOME SYMMETRY IDENTITIES FOR GENERALIZED TWISTED BERNOULLI POLYNOMIALS TWISTED BY UNRAMIFIED ROOTS OF UNITY. Bulletin of the Korean Mathematical Society 52:2, pages 603-618.
Crossref
Dae San Kim & Taekyun Kim. (2015) Umbral calculus associated with Bernoulli polynomials. Journal of Number Theory 147, pages 871-882.
Crossref
Dae San Kim & Taekyun Kim. (2015) Three variable symmetric identities involving Carlitz-type $$q$$ q -Euler polynomials. Mathematical Sciences 8:4, pages 147-152.
Crossref
Serkan Araci, Mehmet Acikgoz & Erdoğan Şen. (2014) On the von Staudt–Clausen’s theorem associated with q-Genocchi numbers. Applied Mathematics and Computation 247, pages 780-785.
Crossref
T. Kim & T. Mansour. (2014) Umbral calculus associated with Frobenius-type Eulerian polynomials. Russian Journal of Mathematical Physics 21:4, pages 484-493.
Crossref
Jin-Woo Son. (2014) IDENTITIES OF SYMMETRY FOR THE HIGHER ORDER q-BERNOULLI POLYNOMIALS. Journal of the Korean Mathematical Society 51:5, pages 1045-1073.
Crossref
Dae San Kim & Taekyun Kim. (2014) A study on the integral of the product of several Bernoulli polynomials. Rocky Mountain Journal of Mathematics 44:4.
Crossref
Dae San Kim & Taekyun Kim. (2014) Some identities of symmetry for the generalized q-Euler polynomials. Applied Mathematics and Computation 235, pages 408-411.
Crossref
Serkan Araci, Erdoğan Şen & Mehmet Acikgoz. (2014) THEOREMS ON GENOCCHI POLYNOMIALS OF HIGHER ORDER ARISING FROM GENOCCHI BASIS. Taiwanese Journal of Mathematics 18:2.
Crossref
D. V. Dolgy, D. S. Kim, T. G. Kim & J. J. Seo. (2014) Identities of Symmetry for Higher-Order Generalized -Euler Polynomials . Abstract and Applied Analysis 2014, pages 1-6.
Crossref
Dae San Kim, Taekyun Kim, Dmitry V Dolgy & Seog-Hoon Rim. (2013) Some new identities of Bernoulli, Euler and Hermite polynomials arising from umbral calculus. Advances in Difference Equations 2013:1.
Crossref
Veli Kurt. (2013) Some symmetry identities for the Apostol-type polynomials related to multiple alternating sums. Advances in Difference Equations 2013:1.
Crossref
Taekyun Kim, Toufik Mansour, Seog-Hoon Rim & Sang-Hun Lee. (2013) Apostol-Euler polynomials arising from umbral calculus. Advances in Difference Equations 2013:1.
Crossref
Yuan He. (2013) Symmetric identities for Carlitz’s q-Bernoulli numbers and polynomials. Advances in Difference Equations 2013:1.
Crossref
Dae San Kim, Taekyun Kim, Seog-Hoon Rim & Dmitry V Dolgy. (2013) Sheffer sequences of polynomials and their applications. Advances in Difference Equations 2013:1.
Crossref
Dae San Kim & Taekyun Kim. (2013) A note on higher-order Bernoulli polynomials. Journal of Inequalities and Applications 2013:1.
Crossref
Serkan Araci, Mehmet Acikgoz & Erdoğan Şen. (2013) On the extended Kimʼs p -adic q -deformed fermionic integrals in the p -adic integer ring. Journal of Number Theory 133:10, pages 3348-3361.
Crossref
Daeyeoul Kim & Min-Soo Kim. (2013) Some symmetric identities on higher order q-Euler polynomials and multivariate fermionic p-adic q-integral on . Applied Mathematics and Computation 221, pages 558-567.
Crossref
A. Bayad & Y. Simsek. (2013) Values of twisted Barnes zeta functions at negative integers. Russian Journal of Mathematical Physics 20:2, pages 129-137.
Crossref
Yuan He & Wenpeng Zhang. (2013) A NOTE ON THE TWISTED LERCH TYPE EULER ZETA FUNCTIONS. Bulletin of the Korean Mathematical Society 50:2, pages 659-665.
Crossref
S. Gaboury, R. Tremblay & J. Fugere. (2013) SYMMETRY PROPERTIES FOR A UNIFIED CLASS OF POLYNOMIALS ATTACHED TO χ. Journal of applied mathematics & informatics 31:1_2, pages 119-130.
Crossref
Dae San Kim & Kyoung Ho Park. (2013) Identities of symmetry for Bernoulli polynomials arising from quotients of Volkenborn integrals invariant under S3. Applied Mathematics and Computation 219:10, pages 5096-5104.
Crossref
Dae San Kim & Taekyun Kim. (2012) Applications of Umbral Calculus Associated with -Adic Invariant Integrals on . Abstract and Applied Analysis 2012, pages 1-12.
Crossref
Imju Lee & Dae San Kim. (2012) Derivation of Identities Involving Bernoulli and Euler Numbers. International Journal of Mathematics and Mathematical Sciences 2012, pages 1-14.
Crossref
D. S. Kim, T. Kim, J. Choi & Y. H. Kim. (2012) Some Identities on Bernoulli and Euler Numbers. Discrete Dynamics in Nature and Society 2012, pages 1-12.
Crossref
Daeyeoul Kim & Min-Soo Kim. (2012) Symmetry Fermionic -Adic -Integral on for Eulerian Polynomials. International Journal of Mathematics and Mathematical Sciences 2012, pages 1-7.
Crossref
Dae San Kim, Dmitry V. Dolgy, Hyun-Mee Kim, Sang-Hun Lee & Taekyun Kim. (2012) Integral Formulae of Bernoulli Polynomials. Discrete Dynamics in Nature and Society 2012, pages 1-15.
Crossref
Seog-Hoon Rim, Joohee Jeong & Sun-Jung Lee. (2012) Identities on the Bernoulli and Genocchi Numbers and Polynomials. International Journal of Mathematics and Mathematical Sciences 2012, pages 1-9.
Crossref
Dae San Kim, Nari Lee, Jiyoung Na & Kyoung Ho Park. (2011) Identities of symmetry for higher-order Euler polynomials in three variables (II). Journal of Mathematical Analysis and Applications 379:1, pages 388-400.
Crossref
Dae San Kim. (2011) Identities of Symmetry for q-Euler Polynomials. Open Journal of Discrete Mathematics 01:01, pages 22-31.
Crossref
Dae San Kim, Taekyun Kim, Sang-Hun Lee, D. V. Dolgy & Seog-Hoon Rim. (2011) Some New Identities on the Bernoulli and Euler Numbers. Discrete Dynamics in Nature and Society 2011, pages 1-11.
Crossref
Dae San Kim. (2011) Identities of Symmetry for Generalized Euler Polynomials. International Journal of Combinatorics 2011, pages 1-12.
Crossref
Dae San Kim. (2010) Identities of symmetry for -Bernoulli polynomials . Computers & Mathematics with Applications 60:8, pages 2350-2359.
Crossref
Eun-Jung Moon, Seog-Hoon Rim, Jeong-Hee Jin & Sun-Jung Lee. (2010) On the Symmetric Properties of Higher-Order Twisted -Euler Numbers and Polynomials. Advances in Difference Equations 2010:1, pages 765259.
Crossref
DaeSan Kim & KyoungHo Park. (2010) Identities of Symmetry for Euler Polynomials Arising from Quotients of Fermionic Integrals Invariant under. Journal of Inequalities and Applications 2010:1, pages 851521.
Crossref
Eun-Jung Moon, Seog-Hoon Rim, Jeong-Hee Jin & Sun-Jung Lee. (2010) On the Symmetric Properties of Higher-Order Twisted q-Euler Numbers and Polynomials. Advances in Difference Equations 2010, pages 1-9.
Crossref
Taekyun Kim, Kyung-Won Hwang & Byungje Lee. (2009) A Note on the q-Euler Measures. Advances in Difference Equations 2009, pages 1-8.
Crossref
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.
Crossref
Lee-Chae Jang. (2009) A Note on H?lder Type Inequality for the Fermionic -Adic Invariant -Integral. Journal of Inequalities and Applications 2009:1, pages 357349.
Crossref
Taekyun Kim, Kyung-Won Hwang & Young-Hee Kim. (2009) Symmetry Properties of Higher-Order Bernoulli Polynomials. Advances in Difference Equations 2009, pages 1-6.
Crossref
Taekyun Kim, Kyoung Ho Park & Kyung-won Hwang. (2009) On the Identities of Symmetry for the ζ-Euler Polynomials of Higher Order. Advances in Difference Equations 2009, pages 1-9.
Crossref
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.
Crossref
KyoungHo Park & Young-Hee Kim. (2008) On Some Arithmetical Properties of the Genocchi Numbers and Polynomials. Advances in Difference Equations 2008:1, pages 195049.
Crossref

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Order Reprints Request Corporate Permissions

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

Request Academic Permissions

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.

Related research

People also read lists articles that other readers of this article have read.

Recommended articles lists articles that we recommend and is powered by our AI driven recommendation engine.

Cited by lists all citing articles based on Crossref citations.
Articles with the Crossref icon will open in a new tab.