Some Symmetric Properties and Location Conjecture of Approximate Roots for (<i>p</i>,<i>q</i>)-Cosine Euler Polynomials

• Main Authors: Cheon Seoung Ryoo, Jung Yoog Kang
• Format: Article
• Language: English
• Published: MDPI AG 2021-08-01
• Series: Symmetry
• Subjects: (<i>p</i>,<i>q</i>)-numbers; (<i>p</i>,<i>q</i>)-exponential functions; (<i>p</i>,<i>q</i>)-cosine Euler polynomials; approximate roots
• Online Access: https://www.mdpi.com/2073-8994/13/8/1520
• ISSN: 2073-8994

In this paper, we introduce <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>p</mi><mo>,</mo><mi>q</mi><mo>)</mo></mrow></semantics></math></inline-formula>-cosine Euler polynomials. From these polynomials, we find several properties and identities. Moreover, we find the circle equations of approximate roots for <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>p</mi><mo>,</mo><mi>q</mi><mo>)</mo></mrow></semantics></math></inline-formula>-cosine Euler polynomials by using a computer.