Symmetric Identities for Carlitz-Type Higher-Order Degenerate (<i>p</i>,<i>q</i>)-Euler Numbers and Polynomials
The main goal of this paper is to investigate some interesting symmetric identities for Carlitz-type higher-order degenerate <inline-formula> <math display="inline"> <semantics> <mrow> <mo>(</mo> <mi>p</mi> <mo>,</mo> <mi>q&...
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| Format: | Article |
| Language: | English |
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MDPI AG
2019-11-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/11/12/1432 |
| _version_ | 1811304629262090240 |
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| author | Kyung-Won Hwang Cheon Seoung Ryoo |
| author_facet | Kyung-Won Hwang Cheon Seoung Ryoo |
| author_sort | Kyung-Won Hwang |
| collection | DOAJ |
| description | The main goal of this paper is to investigate some interesting symmetric identities for Carlitz-type higher-order degenerate <inline-formula> <math display="inline"> <semantics> <mrow> <mo>(</mo> <mi>p</mi> <mo>,</mo> <mi>q</mi> <mo>)</mo> </mrow> </semantics> </math> </inline-formula>-Euler numbers, and polynomials. At first, the Carlitz-type higher-order degenerate <inline-formula> <math display="inline"> <semantics> <mrow> <mo>(</mo> <mi>p</mi> <mo>,</mo> <mi>q</mi> <mo>)</mo> </mrow> </semantics> </math> </inline-formula>-Euler numbers and polynomials are defined. We give few new symmetric identities for Carlitz-type higher-order degenerate <inline-formula> <math display="inline"> <semantics> <mrow> <mo>(</mo> <mi>p</mi> <mo>,</mo> <mi>q</mi> <mo>)</mo> </mrow> </semantics> </math> </inline-formula>-Euler numbers and polynomials. |
| first_indexed | 2024-04-13T08:10:49Z |
| format | Article |
| id | doaj.art-da79c423754f4d37835b1c9ee6724964 |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-04-13T08:10:49Z |
| publishDate | 2019-11-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-da79c423754f4d37835b1c9ee67249642022-12-22T02:55:01ZengMDPI AGSymmetry2073-89942019-11-011112143210.3390/sym11121432sym11121432Symmetric Identities for Carlitz-Type Higher-Order Degenerate (<i>p</i>,<i>q</i>)-Euler Numbers and PolynomialsKyung-Won Hwang0Cheon Seoung Ryoo1Department of Mathematics, Dong-A University, Busan 49315, KoreaDepartment of Mathematics, Hannam University, Daejeon 34430, KoreaThe main goal of this paper is to investigate some interesting symmetric identities for Carlitz-type higher-order degenerate <inline-formula> <math display="inline"> <semantics> <mrow> <mo>(</mo> <mi>p</mi> <mo>,</mo> <mi>q</mi> <mo>)</mo> </mrow> </semantics> </math> </inline-formula>-Euler numbers, and polynomials. At first, the Carlitz-type higher-order degenerate <inline-formula> <math display="inline"> <semantics> <mrow> <mo>(</mo> <mi>p</mi> <mo>,</mo> <mi>q</mi> <mo>)</mo> </mrow> </semantics> </math> </inline-formula>-Euler numbers and polynomials are defined. We give few new symmetric identities for Carlitz-type higher-order degenerate <inline-formula> <math display="inline"> <semantics> <mrow> <mo>(</mo> <mi>p</mi> <mo>,</mo> <mi>q</mi> <mo>)</mo> </mrow> </semantics> </math> </inline-formula>-Euler numbers and polynomials.https://www.mdpi.com/2073-8994/11/12/1432euler numbers and polynomialsdegenerate euler numbers and polynomialscarlitz-type degenerate (p,q)-euler numbers and polynomialscarlitz-type higher-order degenerate (p,q)-euler numbers and polynomialssymmetric identities |
| spellingShingle | Kyung-Won Hwang Cheon Seoung Ryoo Symmetric Identities for Carlitz-Type Higher-Order Degenerate (<i>p</i>,<i>q</i>)-Euler Numbers and Polynomials Symmetry 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 |
| title | Symmetric Identities for Carlitz-Type Higher-Order Degenerate (<i>p</i>,<i>q</i>)-Euler Numbers and Polynomials |
| title_full | Symmetric Identities for Carlitz-Type Higher-Order Degenerate (<i>p</i>,<i>q</i>)-Euler Numbers and Polynomials |
| title_fullStr | Symmetric Identities for Carlitz-Type Higher-Order Degenerate (<i>p</i>,<i>q</i>)-Euler Numbers and Polynomials |
| title_full_unstemmed | Symmetric Identities for Carlitz-Type Higher-Order Degenerate (<i>p</i>,<i>q</i>)-Euler Numbers and Polynomials |
| title_short | Symmetric Identities for Carlitz-Type Higher-Order Degenerate (<i>p</i>,<i>q</i>)-Euler Numbers and Polynomials |
| title_sort | symmetric identities for carlitz type higher order degenerate i p i i q i euler numbers and polynomials |
| topic | 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 |
| url | https://www.mdpi.com/2073-8994/11/12/1432 |
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