On Genocchi Numbers and Polynomials
Seog-Hoon Rim, Kyoung Ho Park, and Eun Jung Moon
Source: Abstr. Appl. Anal. Volume 2008
(2008), Article ID
898471, 7 pages.
Abstract
The main purpose of this paper is to study the distribution of Genocchi polynomials. Finally, we construct the Genocchi zeta function which interpolates Genocchi polynomials at negative integers.
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Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.aaa/1234298989
Digital Object Identifier: doi:10.1155/2008/898471
Mathematical Reviews number (MathSciNet): MR2439256
Zentralblatt MATH identifier: 05352109
References
T. Kim, ``Euler numbers and polynomials associated with zeta functions,'' Abstract and Applied Analysis, vol. 2008, Article ID 581582, 11 pages, 2008.
Mathematical Reviews (MathSciNet): MR2407279
Zentralblatt MATH: 1145.11019
T. Kim, ``The modified $q$-Euler numbers and polynomials,'' Advanced Studies in Contemporary Mathematics, vol. 16, no. 2, pp. 161--170, 2008.
Mathematical Reviews (MathSciNet): MR2404632
T. Kim, ``A note on $p$-adic $q$-integral on $\mathbbZ_p$ associated with $q$-Euler numbers,'' Advanced Studies in Contemporary Mathematics, vol. 15, no. 2, pp. 133--137, 2007.
Mathematical Reviews (MathSciNet): MR2356172
Zentralblatt MATH: 1132.11369
T. Kim, ``$q$-Volkenborn integration,'' Russian Journal of Mathematical Physics, vol. 9, no. 3, pp. 288--299, 2002.
Mathematical Reviews (MathSciNet): MR1965383
Zentralblatt MATH: 1092.11045
T. Kim and Y. Simsek, ``Analytic continuation of the multiple Daehee $q$-$l$-functions associated with Daehee numbers,'' Russian Journal of Mathematical Physics, vol. 15, no. 1, pp. 58--65, 2008.
Mathematical Reviews (MathSciNet): MR2390695
Digital Object Identifier: doi:10.1134/S1061920808040055
Zentralblatt MATH: 05628009
T. Kim, ``$q$-Bernoulli numbers and polynomials associated with Gaussian binomial coefficients,'' Russian Journal of Mathematical Physics, vol. 15, no. 1, pp. 51--57, 2008.
Mathematical Reviews (MathSciNet): MR2390694
Digital Object Identifier: doi:10.1134/S1061920808040055
Zentralblatt MATH: 05628008
T. Kim, ``$q$-extension of the Euler formula and trigonometric functions,'' Russian Journal of Mathematical Physics, vol. 14, no. 3, pp. 275--278, 2007.
Mathematical Reviews (MathSciNet): MR2341775
Digital Object Identifier: doi:10.1134/S1061920807030041
Zentralblatt MATH: 05627977
T. Kim, J. Y. Choi, and J. Y. Sug, ``Extended $q$-Euler numbers and polynomials associated with fermionic $p$-adic $q$-integral on $\mathbbZ_p$,'' Russian Journal of Mathematical Physics, vol. 14, no. 2, pp. 160--163, 2007.
Mathematical Reviews (MathSciNet): MR2318827
Zentralblatt MATH: 1132.33331
Digital Object Identifier: doi:10.1134/S1061920807020045
S.-H. Rim and T. Kim, ``A note on $p$-adic Euler measure on $\mathbbZ_p$,'' Russian Journal of Mathematical Physics, vol. 13, no. 3, pp. 358--361, 2006.
Mathematical Reviews (MathSciNet): MR2262837
Zentralblatt MATH: 1163.11348
Digital Object Identifier: doi:10.1134/S1061920806030113
T. Kim, ``$q$-generalized Euler numbers and polynomials,'' Russian Journal of Mathematical Physics, vol. 13, no. 3, pp. 293--298, 2006.
Mathematical Reviews (MathSciNet): MR2262831
Zentralblatt MATH: 1163.11311
Digital Object Identifier: doi:10.1134/S1061920806030058
T. Kim, ``Multiple $p$-adic $L$-function,'' Russian Journal of Mathematical Physics, vol. 13, no. 2, pp. 151--157, 2006.
Mathematical Reviews (MathSciNet): MR2262821
Zentralblatt MATH: 1140.11352
Digital Object Identifier: doi:10.1134/S1061920806020038
H. M. Srivastava, T. Kim, and Y. Simsek, ``$q$-Bernoulli numbers and polynomials associated with multiple $q$-zeta functions and basic $L$-series,'' Russian Journal of Mathematical Physics, vol. 12, no. 2, pp. 241--268, 2005.
T. Kim, ``Power series and asymptotic series associated with the $q$-analog of the two-variable $p$-adic $L$-function,'' Russian Journal of Mathematical Physics, vol. 12, no. 2, pp. 186--196, 2005.
T. Kim, ``Analytic continuation of multiple $q$-zeta functions and their values at negative integers,'' Russian Journal of Mathematical Physics, vol. 11, no. 1, pp. 71--76, 2004.
Mathematical Reviews (MathSciNet): MR2134649
Zentralblatt MATH: 1115.11068
T. Kim, ``Non-Archimedean $q$-integrals associated with multiple Changhee $q$-Bernoulli polynomials,'' Russian Journal of Mathematical Physics, vol. 10, no. 1, pp. 91--98, 2003.
Mathematical Reviews (MathSciNet): MR2013106
Zentralblatt MATH: 1072.11090
T. Kim, ``On Euler-Barnes multiple zeta functions,'' Russian Journal of Mathematical Physics, vol. 10, no. 3, pp. 261--267, 2003.
Mathematical Reviews (MathSciNet): MR2012900
Zentralblatt MATH: 1038.11058
T. Kim, L.-C. Jang, and H. K. Pak, ``A note on $q$-Euler and Genocchi numbers,'' Proceedings of the Japan Academy. Series A, vol. 77, no. 8, pp. 139--141, 2001.
Mathematical Reviews (MathSciNet): MR1863659
Zentralblatt MATH: 0997.11017
Digital Object Identifier: doi:10.3792/pjaa.77.139
Project Euclid: euclid.pja/1148393021
T. Kim, ``A note on $q$-Volkenborn integration,'' Proceedings of the Jangjeon Mathematical Society, vol. 8, no. 1, pp. 13--17, 2005.
T. Kim, ``On the $q$-extension of Euler and Genocchi numbers,'' Journal of Mathematical Analysis and Applications, vol. 326, no. 2, pp. 1458--1465, 2007.
Mathematical Reviews (MathSciNet): MR2280996
Zentralblatt MATH: 1112.11012
Digital Object Identifier: doi:10.1016/j.jmaa.2006.03.037
T. Kim, ``A note on the $q$-Genocchi numbers and polynomials,'' Journal of Inequalities and Applications, vol. 2007, Article ID 71452, 8 pages, 2007.
T. Kim, et al., Introduction to Non-Archimedian Analysis, Seoul, Korea, Kyo Woo Sa, 2004.
L.-C. Jang and T. Kim, ``$q$-Genocchi numbers and polynomials associated with fermionic $p$-adic invariant integrals on $\mathbbZ_p$,'' Abstract and Applied Analysis, vol. 2008, Article ID 232187, 8 pages, 2008.
Mathematical Reviews (MathSciNet): MR2407281
Zentralblatt MATH: 1149.11010
L.-C. Jang, T. Kim, D.-H. Lee, and D.-W. Park, ``An application of polylogarithms in the analogs of Genocchi numbers,'' Notes on Number Theory and Discrete Mathematics, vol. 7, no. 3, pp. 65--69, 2001.
Mathematical Reviews (MathSciNet): MR2020979
M. Cenkci, M. Can, and V. Kurt, ``$p$-adic interpolation functions and Kummer-type congruences for $q$-twisted and $q$-generalized twisted Euler numbers,'' Advanced Studies in Contemporary Mathematics, vol. 9, no. 2, pp. 203--216, 2004.
Mathematical Reviews (MathSciNet): MR2090123
Zentralblatt MATH: 1083.11016
H. Ozden, Y. Simsek, S.-H. Rim, and I. N. Cangul, ``A note on $p$-adic $q$-Euler measure,'' Advanced Studies in Contemporary Mathematics, vol. 14, no. 2, pp. 233--239, 2007.
Mathematical Reviews (MathSciNet): MR2316989
Y. Simsek, ``On $p$-adic twisted $q$-$L$-functions related to generalized twisted Bernoulli numbers,'' Russian Journal of Mathematical Physics, vol. 13, no. 3, pp. 340--348, 2006.
Mathematical Reviews (MathSciNet): MR2262835
Zentralblatt MATH: 1163.11312
Digital Object Identifier: doi:10.1134/S1061920806030095
Y. Simsek, I. N. Cangul, V. Kurt, and D. Kim, ``$q$-Genocchi numbers and polynomials associated with $q$-Genocchi-type $l$-functions,'' Advances in Difference Equations, vol. 2008, Article ID 815750, 12 pages, 2008.
Mathematical Reviews (MathSciNet): MR2407436
Zentralblatt MATH: 1140.33308
Digital Object Identifier: doi:10.1155/2008/815750
M. Schork, ``Combinatorial aspects of normal ordering and its connection to $q$-calculus,'' Advanced Studies in Contemporary Mathematics, vol. 15, no. 1, pp. 49--57, 2007.
Mathematical Reviews (MathSciNet): MR2339378
M. Schork, ``Ward's ``calculus of sequences'', $q$-calculus and the limit $q\rightarrow -1$,'' Advanced Studies in Contemporary Mathematics, vol. 13, no. 2, pp. 131--141, 2006.
Mathematical Reviews (MathSciNet): MR2264303
Zentralblatt MATH: 1111.05010
K. Shiratani and S. Yamamoto, ``On a $p$-adic interpolation function for the Euler numbers and its derivatives,'' Memoirs of the Faculty of Science. Kyushu University. Series A, vol. 39, no. 1, pp. 113--125, 1985.
Mathematical Reviews (MathSciNet): MR783226
Zentralblatt MATH: 0574.12017
Digital Object Identifier: doi:10.2206/kyushumfs.39.113
Abstract and Applied Analysis