Symmetric Identities for Carlitz’s Type Higher-Order (<i>p</i>,<i>q</i>)-Genocchi Polynomials

• Main Authors: Ahyun Kim, Cheon Seoung Ryoo
• Format: Article
• Language: English
• Published: MDPI AG 2020-10-01
• Series: Symmetry
• Subjects: higher-order (<i>p</i>,<i>q</i>)-Genocchi polynomials; symmetric identities; alternating power sums
• Online Access: https://www.mdpi.com/2073-8994/12/10/1670

In this paper, we study Carlitz’s type higher-order <inline-formula><math display="inline"><semantics><mrow><mo>(</mo><mi>p</mi><mo>,</mo><mi>q</mi><mo>)</mo></mrow></semantics></math></inline-formula>-Genocchi polynomials. To be specific, we define Carlitz’s type higher-order <inline-formula><math display="inline"><semantics><mrow><mo>(</mo><mi>p</mi><mo>,</mo><mi>q</mi><mo>)</mo></mrow></semantics></math></inline-formula>-Genocchi polynomials and Carlitz’s type higher-order <inline-formula><math display="inline"><semantics><mrow><mo>(</mo><mi>h</mi><mo>,</mo><mi>p</mi><mo>,</mo><mi>q</mi><mo>)</mo></mrow></semantics></math></inline-formula>-Genocchi polynomials. This paper also explores properties including distribution relation and symmetric identities. In addition, we find alternating <inline-formula><math display="inline"><semantics><mrow><mo>(</mo><mi>p</mi><mo>,</mo><mi>q</mi><mo>)</mo></mrow></semantics></math></inline-formula>-power sums. We identify symmetric identities using Carlitz’s type higher-order <inline-formula><math display="inline"><semantics><mrow><mo>(</mo><mi>h</mi><mo>,</mo><mi>p</mi><mo>,</mo><mi>q</mi><mo>)</mo></mrow></semantics></math></inline-formula>-Genocchi polynomials and alternating <inline-formula><math display="inline"><semantics><mrow><mo>(</mo><mi>p</mi><mo>,</mo><mi>q</mi><mo>)</mo></mrow></semantics></math></inline-formula>-power sums.