×

Some identities of the Frobenius-Euler polynomials. (English) Zbl 1246.11052

Summary: By using the ordinary fermionic \(p\)-adic invariant integral on \(\mathbb Z_p\), we derive some interesting identities related to the Frobenius-Euler polynomials.

MSC:

11B68 Bernoulli and Euler numbers and polynomials
11S80 Other analytic theory (analogues of beta and gamma functions, \(p\)-adic integration, etc.)
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] T. Kim, “q-Volkenborn integration,” Russian Journal of Mathematical Physics, vol. 9, no. 3, pp. 288-299, 2002. · Zbl 1092.11045
[2] T. Kim, “A note on p-adic q-integral on \Bbb Zp associated with q-Euler numbers,” Advanced Studies in Contemporary Mathematics, vol. 15, no. 2, pp. 133-137, 2007. · Zbl 1132.11369
[3] T. Kim, “On p-adic interpolating function for q-Euler numbers and its derivatives,” Journal of Mathematical Analysis and Applications, vol. 339, no. 1, pp. 598-608, 2008. · Zbl 1160.11013 · doi:10.1016/j.jmaa.2007.07.027
[4] T. Kim, “q-extension of the Euler formula and trigonometric functions,” Russian Journal of Mathematical Physics, vol. 14, no. 3, pp. 275-278, 2007. · Zbl 1188.33001 · doi:10.1134/S1061920807030041
[5] 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. · Zbl 1190.11049
[6] 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. · Zbl 1072.11090
[7] T. Kim, “q-Euler numbers and polynomials associated with p-adic q-integrals,” Journal of Nonlinear Mathematical Physics, vol. 14, no. 1, pp. 15-27, 2007. · Zbl 1158.11009 · doi:10.2991/jnmp.2007.14.1.3
[8] B. A. Kupershmidt, “Reflection symmetries of q-Bernoulli polynomials,” Journal of Nonlinear Mathematical Physics, vol. 12, supplement 1, pp. 412-422, 2005. · Zbl 1362.33021 · doi:10.2991/jnmp.2005.12.s1.34
[9] 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. · Zbl 1143.11008
[10] 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. · Zbl 1111.05010
[11] 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. · Zbl 1141.05019
[12] 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. · Zbl 1163.11312 · doi:10.1134/S1061920806030095
[13] Y. Simsek, “Theorems on twisted L-function and twisted Bernoulli numbers,” Advanced Studies in Contemporary Mathematics, vol. 11, no. 2, pp. 205-218, 2005. · Zbl 1178.11058
[14] Y. Simsek, “q-Dedekind type sums related to q-zeta function and basic L-series,” Journal of Mathematical Analysis and Applications, vol. 318, no. 1, pp. 333-351, 2006. · Zbl 1149.11054 · doi:10.1016/j.jmaa.2005.06.007
[15] T. Kim, “The modified q-Euler numbers and polynomials,” Advanced Studies in Contemporary Mathematics, vol. 16, no. 2, pp. 161-170, 2008. · Zbl 1172.11006
[16] T. Kim, “Euler numbers and polynomials associated with zeta functions,” Abstract and Applied Analysis, vol. 2008, Article ID 581582, 11 pages, 2008. · Zbl 1145.11019 · doi:10.1155/2008/581582
[17] T. Kim, “An identity of the symmetry for the Frobenius-Euler polynomials associated with the fermionic p-adic invariant q-integrals on \Bbb Zp,” to appear in The Rocky Mountain Journal of Mathematics.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.