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ADVANCED STUDIES IN THEORETICAL PHYSICS ISSN 1313-1311 (print) ISSN 1314-7609 (online) |
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C. S. Ryoo A note on the tangent numbers and polynomials Adv. Studies Theor. Phys., Vol. 7, 2013, no. 9-12, 447-454 http://dx.doi.org/10.12988/astp.2013.13042 Copyright © 2013 C. S. Ryoo. This article is distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Cited by (46): Cheon Seoung Ryoo, Some identities involving modified degenerate tangent numbers and polynomials, Global Journal of Pure and Applied Mathematics, 12 (2016), no. 3, 2621-2630 [View at Publisher] Cheon Seoung Ryoo, Some properties of two dimensional q-tangent numbers and polynomials, Global Journal of Pure and Applied Mathematics, 12 (2016), no. 4, 2999-3007 [View at Publisher] Cheon Seoung Ryoo, Modified degenerate tangent numbers and polynomials, Global Journal of Pure and Applied Mathematics, 12 (2016), no. 2, 1567-1574 [View at Publisher] Cheon Seoung Ryoo, Notes on Degenerate Twisted (h,q)-Tangent Numbers and Polynomials Associated with the p-Adic Integral on Zp, International Journal of Mathematical Analysis, 10 (2016), no. 7, 313-321 [CrossRef] C. S. Ryoo, Carlitz’s Type Twisted (h, q)-Tangent Numbers and Polynomials, Applied Mathematical Sciences, 9 (2015), no. 30, 1475-1482 [CrossRef] C. S. Ryoo, On the Degenerate q-Tangent Numbers and Polynomials Associated with the p-Adic Integral on Zp, International Journal of Mathematical Analysis, 9 (2015), no. 52, 2571-2579 [CrossRef] C. S. Ryoo, Symmetric Properties for the Degenerate Tangent Polynomials Associated with p-Adic Integral on Z_p, Applied Mathematical Sciences, 9 (2015), no. 142, 7071-7079 [CrossRef] C. S. Ryoo, On the Symmetric Properties for the Generalized Twisted q-Tangent Numbers and Polynomials, Advanced Studies in Theoretical Physics, 9 (2015), no. 2, 63-69 [CrossRef] C. S. Ryoo, Symmetric Identities for Carlitz’s Twisted q-Tangent Numbers and Polynomials Associated with Fermionic p-Adic Integral on Z_p, Far East Journal of Mathematical Sciences, 98 (2015), no. 6, 699-706 [CrossRef] C. S. Ryoo, Zeros of the Degenerate Tangent Polynomials, Applied Mathematical Sciences, 9 (2015), no. 131, 6521-6528 [CrossRef] C. S. Ryoo, A Note on q-Extension of Twisted Tangent Numbers and Polynomials Associated with the p-Adic q-Integral on Z_p, Advanced Studies in Theoretical Physics, 9 (2015), no. 6, 273-279 [CrossRef] C. S. Ryoo, On Degenerate Twisted q-Tangent Numbers and Polynomials Associated with the p-Adic Integral on Zp, International Journal of Algebra, 9 (2015), no. 12, 511-519 [CrossRef] C. S. Ryoo, q-Extension of Tangent Numbers and Polynomials Associated with the p-Adic q-Integral on Zp, International Journal of Mathematical Analysis, 9 (2015), no. 14, 647-653 [CrossRef] C. S. Ryoo, Symmetric Identities for Carlitz’s Type Twisted Tangent Polynomials Using Twisted Tangent Zeta Function, Applied Mathematical Sciences, 9 (2015), no. 30, 1483-1489 [CrossRef] C. S. Ryoo, On Carlitz’s Type Twisted q-Tangent Numbers and Polynomials Associated with p-adic Integral on Zp, International Journal of Mathematical Analysis, 9 (2015), no. 5, 225-230 [CrossRef] Cheon Seoung Ryoo, On the generalized degenerate tangent numbers and polynomials, Turkish Journal of Analysis and Number Theory, 3 (2015), no. 4, 104-107 [CrossRef] C. S. Ryoo, Numerical Investigation of the Zeros of q-Extension of Tangent Polynomials, Applied Mathematical Sciences, 9 (2015), no. 52, 2553-2558 [CrossRef] C. S. Ryoo, On Carlitz’s type twisted tangent numbers and polynomials associated with p-adic integral on Z_p, Applied Mathematical Sciences, 8 (2014), no. 76, 3763-3769 [CrossRef] Cemile Bildirici, Mehmet Acikgoz and Serkan Araci, A note on analogues of Tangent polynomials, Journal for Algebra and Number Theory Academia, 4 (2014), no. 1, 21-29 [View at Publisher] C. S. Ryoo, A Note on the Carlitz’s Type (h,q)-Tangent Numbers and Polynomials Associated with p-adic Integral on Z_p, Applied Mathematical Sciences, 8 (2014), no. 106, 5277-5283 [CrossRef] C. S. Ryoo, A Note on Generalized Twisted (h,q)-Tangent Numbers and Polynomials, Applied Mathematical Sciences, 8 (2014), no. 120, 6005-6010 [CrossRef] C. S. Ryoo, Generalized (h,q)-Tangent Numbers and Polynomials, Applied Mathematical Sciences, 8 (2014), no. 49, 2439-2445 [CrossRef] C. S. Ryoo, On Generalized Twisted q-Tangent Numbers and Polynomials, International Journal of Mathematical Analysis, 8 (2014), no. 36, 1751-1756 [CrossRef] C. S. Ryoo, Multiple Tangent zeta function and Tangent polynomials of higher order, Adv. Studies Theor. Phys., 8 (2014), no. 10, 457-462 [CrossRef] C. S. Ryoo, Structure of the Zeros of the Twisted q-Tangent Polynomials, Int. Journal of Math. Analysis, 8 (2014), no. 25, 1213-1218 [CrossRef] C. S. Ryoo, Symmetric Identities for Carlitz’s q-Tangent Polynomials Using q-Tangent Zeta Function, Applied Mathematical Sciences, 8 (2014), no. 76, 3771-3778 [CrossRef] C. S. Ryoo, A Note on the Twisted (h,q)-Tangent Numbers and Polynomials Associated with the p-Adic Integral on Z_p, Adv. Studies Theor. Phys., 8 (2014), no. 3, 143-149 [CrossRef] C. S. Ryoo, A Numerical investigation on the zeros of the tangent polynomials, J. Appl. Math. and Informatics, 32 (2014), no. 3-4, 315-322 [CrossRef] C. S. Ryoo, Multiple q-Tangent Zeta Functions and q-Tangent Polynomials, Applied Mathematical Sciences, 8 (2014), no. 76, 3755-3761 [CrossRef] C. S. Ryoo, On the Symmetric Properties for the Generalized Twisted Tangent Polynomials, Advanced Studies in Theoretical Physics, 8 (2014), no. 23, 1043-1049 [CrossRef] C. S. Ryoo, Symmetric Properties for the Twisted (h,q)-Tangent Polynomials Associated with the p-Adic Integral on Z_p, Applied Mathematical Sciences, 8 (2014), no. 49, 2447-2453 [CrossRef] C. S. Ryoo, A Note on the Generalized q-Tangent Polynomials, Adv. Studies Theor. Phys., 8 (2014), no. 1, 43-48 [CrossRef] C. S. Ryoo, A Note on the Symmetric Properties for the q-Twisted Tangent Polynomials, Int. Journal of Math. Analysis, 8 (2014), no. 5, 211-217 [CrossRef] C. S. Ryoo, A Note on the Generalized Twisted Tangent Polynomials, Int. Journal of Math. Analysis, 7 (2013), no. 55, 2717-2722 [CrossRef] C. S. Ryoo, Symmetric Properties for the Twisted Tangent Polynomials, Applied Mathematical Sciences, 7 (2013), no. 121, 6003-6008 [CrossRef] C. S. Ryoo, Numerical Investigation on the Structure of the Zeros of the Twisted Tangent Polynomials, Applied Mathematical Sciences, 7 (2013), no. 121, 5995-6001 [CrossRef] C. S. Ryoo, Symmetric Properties for the q-Tangent Polynomials, Int. Journal of Math. Analysis, 7 (2013), no. 61, 3027-3033, [CrossRef] C. S. Ryoo, On the analogues of Tangent numbers and polynomials associated with p-adic integral on Zp, Applied Mathematical Sciences, 7 (2013), no. 64, 3177-3183 [View at Publisher] C. S. Ryoo, On the (h,q)-Tangent Numbers and Polynomials, Adv. Studies Theor. Phys, 7 (2013), no. 19, 915-921 [CrossRef] C. S. Ryoo, On the twisted q-Tangent numbers and polynomials, Applied Mathematical Sciences, 7 (2013), no. 99, 4935-4941 [CrossRef] C. S. Ryoo, On Carlitz’s Type q-Tangent Numbers Associated with the Fermionic, p-Adic Integral on Z_p, Journal of Algebra, Number Theory and Applications, 31 (2013), no. 2, 91-99 [View at Publisher] C. S. Ryoo, Generalized Tangent numbers and polynomials associated with p-adic integral on Zp, Applied Mathematical Sciences, 7 (2013), no. 99, 4929-4934 [CrossRef] C. S. Ryoo, A note on the symmetric properties for the tangent polynomials, Int. Journal of Math. Analysis, 7 (2013), no. 52, 2575-2581 [CrossRef] C. S. Ryoo, Some relationships between the Tangent polynomials and Bernstein polynomials, Int. J. Math. Anal., 7 (2013), no. 35, 1723-1730 [CrossRef] C. S. Ryoo, Numerical Computations of the Zeros of the q-Tangent Polynomials, Applied Mathematical Sciences, 7 (2013), no. 114, 5675-5681 [CrossRef] C. S. Ryoo, Some Identities on the Bernstein Polynomials and Twisted Tangent Polynomials, Applied Mathematical Sciences, 7 (2013), no. 114, 5667-5673 [CrossRef]
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