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Open AccessArticle

Symmetric Identities for Carlitz-Type Higher-Order Degenerate (p,q)-Euler Numbers and Polynomials

1
Department of Mathematics, Dong-A University, Busan 49315, Korea
2
Department of Mathematics, Hannam University, Daejeon 34430, Korea
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Author to whom correspondence should be addressed.
Symmetry 2019, 11(12), 1432; https://doi.org/10.3390/sym11121432
Received: 18 October 2019 / Revised: 11 November 2019 / Accepted: 18 November 2019 / Published: 20 November 2019
(This article belongs to the Special Issue Polynomials: Special Polynomials and Number-Theoretical Applications)
The main goal of this paper is to investigate some interesting symmetric identities for Carlitz-type higher-order degenerate ( p , q ) -Euler numbers, and polynomials. At first, the Carlitz-type higher-order degenerate ( p , q ) -Euler numbers and polynomials are defined. We give few new symmetric identities for Carlitz-type higher-order degenerate ( p , q ) -Euler numbers and polynomials. View Full-Text
Keywords: Euler numbers and polynomials; degenerate Euler numbers and polynomials; Carlitz-type degenerate (p,q)-Euler numbers and polynomials; Carlitz-type higher-order degenerate (p,q)-Euler numbers and polynomials; symmetric identities Euler numbers and polynomials; degenerate Euler numbers and polynomials; Carlitz-type degenerate (p,q)-Euler numbers and polynomials; Carlitz-type higher-order degenerate (p,q)-Euler numbers and polynomials; symmetric identities
MDPI and ACS Style

Hwang, K.-W.; Ryoo, C.S. Symmetric Identities for Carlitz-Type Higher-Order Degenerate (p,q)-Euler Numbers and Polynomials. Symmetry 2019, 11, 1432.

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