Fourier expansions for higher-order Apostol–Genocchi, Apostol–Bernoulli and Apostol–Euler polynomials

Abstract

Abstract Fourier expansions of higher-order Apostol–Genocchi and Apostol–Bernoulli polynomials are obtained using Laurent series and residues. The Fourier expansion of higher-order Apostol–Euler polynomials is obtained as a consequence.

Keywords

• Fourier expansion
• Bernoulli polynomials
• Euler polynomials
• Genocchi polynomials
• Apostol–Genocchi polynomials
• Apostol–Bernoulli polynomials