IJPAM: Volume 113, No. 3 (2017)

Title

SYMMETRIC IDENTITIES
FOR THE HIGHER-ORDER TWISTED
$(h, q)$-EULER NUMBERS AND POLYNOMIALS

Authors

C.S. Ryoo
Department of Mathematics
Hannam University
Daejeon 306-791, KOREA

Abstract

In this paper we investigate some interesting symmetric identities for twisted $(h, q)$-Euler polynomials of higher order in complex field.

History

Received: December 6, 2016
Revised: February 1, 2017
Published: March 28, 2017

AMS Classification, Key Words

AMS Subject Classification: 11B68, 11S40, 11S80
Key Words and Phrases: Euler numbers and polynomials, $q$-Euler numbers and polynomials, higher order $q$-Euler numbers and polynomials, higher-order twisted $(h, q)$-Euler numbers and polynomials

Download Section

Download paper from here.
You will need Adobe Acrobat reader. For more information and free download of the reader, see the Adobe Acrobat website.

Bibliography

M. Cenkci, The $p$-adic generalized twisted $(h, q)$-Euler-$l$-function and its applications, Adv. Stud. Contemp. Math., 15 (2007), 34-47.D.V. Dolgy, D.S. Kim, T.G. Kim, J.J. Seo, Identities of Symmetry for Higher-Order Generalized $q$-Euler Polynomials, Abstract and Applied Analysis, 2014 (2014), Article ID 286239, 6 pages.Yuan He, Symmetric identities for Carlitz's $q$-Bernoulli numbers and polynomials, Adv. Difference Equ., 246 (2013), 10 pages.D. Kim, T. Kim, J.J. Seo, Identities of symmetric for $(h, q)$-extension of higher-order Euler polynomials, Applied Mathemtical Sciences, 8 (2014), 3799-3808.T. Kim, New approach to $q$-Euler polynomials of higher order, Russ. J. Math. Phys., 17 (2010), 218-225.Y.H. Kim, H.Y. Jung, C.S. Ryoo, On the generalized Euler polynomials of the second kind, J. Appl. Math. & Informatics, 31 (2013), 623 - 630.Y.H. Kim, H.Y. Jung, C.S. Ryoo, An extension of generalized Euler polynomials of the second kind, J. Appl. Math. & Informatics, 32 (2014), 465 - 474.H.Y. Lee, N.S. Jung, J.Y. Kang, C.S. Ryoo, Some identities on the higher-order-twisted $q$-Euler numbers and polynomials with weight $\alpha$, Adv. Difference Equ., 21 (2012), 10 pages.H. Ozden, Y. Simsek, I.N. Cangul, Euler polynomials associated with $p$-adic $q$-Euler measure, Gen. Math., 15 (2007), 24-37.C.S. Ryoo, On the generalized Barnes type multiple $q$-Euler polynomials twisted by ramified roots of unity, Proc. Jangjeon Math. Soc., 13 (2010), 255-263.C.S. Ryoo, A note on the weighted $q$-Euler numbers and polynomials, Adv. Stud. Contemp. Math., 21 (2011), 47-54.Y. Simsek, $q$-analogue of twisted $l$-series and $q$-twisted Euler numbers, Journal of Number Theory, 110 (2005), 267-278.Y. Simsek, Twisted $(h, q)$-Bernoulli numbers and polynomials related to twisted $(h, q)$-zeta function and $L$-function, J.Math. Anal. Appl., 324 (2006), 790-804.

How to Cite?

DOI: 10.12732/ijpam.v113i3.7 How to cite this paper?

Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2017
Volume: 113
Issue: 3
Pages: 455 - 463


$(h, q)$-EULER NUMBERS AND POLYNOMIALS%22&as_occt=any&as_epq=&as_oq=&as_eq=&as_publication=&as_ylo=&as_yhi=&as_sdtAAP=1&as_sdtp=1" title="Click to search Google Scholar for this entry" rel="nofollow">Google Scholar; DOI (International DOI Foundation); WorldCAT.

CC BY This work is licensed under the Creative Commons Attribution International License (CC BY).