Unified Bernoulli-Euler polynomials of Apostol type

2021/01/30 by Hacène Belbachir, Belbachir, Hacène, Yahia Djemmada +3
Mathematics · Physics and Astronomy · #Advanced Mathematical Identities #Historical Astronomy and Related Studies

paper · pdf · doi:10.48550/arxiv.2102.00137

Abstract

The object of this paper is to introduce and study properties of unified Apostol-Bernoulli and Apostol-Euler polynomials noted by \\mathfrakV_n(x;λ;μ)\_{n ≥ 0}. We study some arithmetic properties of \\mathfrakV_n(x;λ;μ)\_{n ≥ 0} as their connection to Apostol-Euler polynomials and Apostol-Bernoulli polynomials. Also, we give derivation and integration representations of \\mathfrakV_n(x;λ;μ)\_{n ≥ 0}. Finally, we use the umbral calculus approach to deduce symmetric identities.

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• The 2-variable unified family of generalized Apostol-Euler, Bernoulli and Genocchi polynomials
• The simultaneous multiplication formulas for Apostol-Bernoulli polynomials and generalized Frobenius-Euler polynomials
• New Extension of Unified Family of Apostol-Type of Polynomials and Numbers
• Two closed forms for the Apostol-Bernoulli polynomials