Choi, Jongsung; Kim, Hyun-Mee; Kim, Young-Hee Some identities on the high-order \(q\)-Euler numbers and polynomials with weight 0. (English) Zbl 1276.34005 Abstr. Appl. Anal. 2013, Article ID 459763, 6 p. (2013). Summary: We construct the \(N\)-th-order nonlinear ordinary differential equation related to the generating function of \(q\)-Euler numbers with weight 0. From this, we derive some identities on \(q\)-Euler numbers and polynomials of higher order with weight 0. Cited in 2 Documents MSC: 34A34 Nonlinear ordinary differential equations and systems 11B68 Bernoulli and Euler numbers and polynomials × Cite Format Result Cite Review PDF Full Text: DOI References: [1] Carlitz, L., Eulerian numbers and polynomials, Mathematics Magazine, 32, 247-260 (1959) · Zbl 0092.06601 · doi:10.2307/3029225 [2] Carlitz, L., The product of two Eulerian polynomials, Mathematics Magazine, 36, 1, 37-41 (1963) · Zbl 0114.03406 · doi:10.2307/2688134 [3] Choi, J., A note on Eulerian polynomials of higher order, Journal of the Chungcheong Mathematical Society, 26, 1, 191-196 (2013) [4] Choi, J.; Kim, T.; Kim, Y. H., A recurrence formula for \(q\)-Euler numbers of higher order, Proceedings of the Jangjeon Mathematical Society, 13, 3, 321-326 (2010) · Zbl 1244.05027 [5] Choi, J.; Kim, T.; Kim, Y.-H., A note on the \(q\)-analogues of Euler numbers and polynomials, Honam Mathematical Journal, 33, 4, 529-534 (2011) · Zbl 1280.11015 · doi:10.5831/HMJ.2011.33.4.529 [6] Kim, D. S., Identities of symmetry for generalized Euler polynomials, International Journal of Combinatorics, 2011 (2011) · Zbl 1262.11022 · doi:10.1155/2011/432738 [7] Kim, D. S.; Kim, T.; Choi, J.; Kim, Y. H., Identities involving \(q\)-Bernoulli and \(q\)-Euler numbers, Abstract and Applied Analysis, 2012 (2012) · Zbl 1242.11016 · doi:10.1155/2012/674210 [8] Kim, H.-M.; Choi, J.; Kim, T., On the extended \(q\)-Euler numbers and polynomials of higher-order with weight, Honam Mathematical Journal, 34, 1, 1-9 (2012) · Zbl 1269.11022 · doi:10.5831/HMJ.2012.34.1.1 [9] Kim, T., Identities involving Frobenius-Euler polynomials arising from non-linear differential equations, Journal of Number Theory, 132, 12, 2854-2865 (2012) · Zbl 1262.11024 · doi:10.1016/j.jnt.2012.05.033 [10] Kim, T.; Choi, J., A note on the product of Frobenius-Euler polynomials arising from the \(p\)-adic integral on \(\Bbb Z_p\), Advanced Studies in Contemporary Mathematics, 22, 2, 215-223 (2012) · Zbl 1252.11021 [11] Kim, T.; Choi, J., On the \(q\)-Euler numbers and polynomials with weight 0, Abstract and Applied Analysis, 2012 (2012) · Zbl 1250.11027 · doi:10.1155/2012/795304 [12] Ozden, H.; Cangul, I. N.; Simsek, Y., Multivariate interpolation functions of higher-order \(q\)-Euler numbers and their applications, Abstract and Applied Analysis, 2008 (2008) · Zbl 1140.11313 · doi:10.1155/2008/390857 [13] Ozden, H.; Simsek, Y., A new extension of \(q\)-Euler numbers and polynomials related to their interpolation functions, Applied Mathematics Letters, 21, 9, 934-939 (2008) · Zbl 1152.11009 · doi:10.1016/j.aml.2007.10.005 [14] Simsek, Y., Complete sum of products of \((h, q)\)-extension of Euler polynomials and numbers, Journal of Difference Equations and Applications, 16, 11, 1331-1348 (2010) · Zbl 1223.11027 · doi:10.1080/10236190902813967 [15] Simsek, Y., Generating functions for \(q\)-Apostol type Frobenius-Euler numbers and polynomials, Axioms, 1, 3, 395-403 (2012) · Zbl 1294.11025 · doi:10. [16] Simsek, Y., Generating functions for generalized Stirling type numbers, Array type polynomials, Eulerian type polynomials and their applications, Fixed Point Theory and Applications, 2013, article 87 (2013) · Zbl 1293.11044 · doi:10.1186/1687-1812-2013-87 [17] Zachmanoglou, C.; Thoe, D. W., Introduction to Partial Differntial Equations with Applications (1976), Baltimore, Md, USA: The Williams and Wilkins company, Baltimore, Md, USA · Zbl 0327.35001 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.