The intended objective of this paper is to introduce a new class of generalized $q$-Hermite based Apostol type polynomials by combining the $q$-Hermite polynomials and a unified family of $q$-Apostol-type polynomials. The generating function, series definition and several explicit representations for these polynomials are established. The $q$-Hermite-Apostol Bernoulli, $q$-Hermite-Apostol Euler and $q$-Hermite-Apostol Genocchi polynomials are studied as special members of this family and corresponding relations for these polynomials are obtained.
$q$-Hermite polynomials Generalized $q$-Apostol type polynomials Generalized $q$-Hermite Apostol type polynomials Explicit representation
Birincil Dil | İngilizce |
---|---|
Konular | Matematik |
Bölüm | Makaleler |
Yazarlar | |
Yayımlanma Tarihi | 22 Mart 2019 |
Gönderilme Tarihi | 28 Ekim 2018 |
Kabul Tarihi | 12 Kasım 2018 |
Yayımlandığı Sayı | Yıl 2019 Cilt: 2 Sayı: 1 |
CAMS'da yayınlanan makaleler Creative Commons Atıf-GayriTicari 4.0 Uluslararası Lisansı ile lisanslanmıştır.