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

Fourier Expansions and Integral Representations for Genocchi Polynomials

In this paper, by using the Lipschitz summation formula, we obtain Fourier expansions and integral representations for the Genocchi polynomials. Some other new and interesting results are also shown.

Higher order Riesz transforms for Hermite expansions

In this paper, we consider the Riesz transform of higher order associated with the harmonic oscillator [Formula: see text], where Δ is the Laplacian on [Formula: see text]. Moreover, the boundedness of Riesz transforms of higher order associated with Hermite functions on the Hardy space is proved.

Higher order Fourier analysis

Higher-order Fourier Analysis and Applications

Higher-order Changhee Numbers and Polynomials

In this paper, we consider the higher-order Changhee numbers and polynomials which are derived from the fermionic p-adic integral on Zp and give some relations between higher-order Changhee polynomials and special polynomials. 366 Dae San Kim, Taekyun Kim, Jong Jin Seo and Sang-Hun Lee