A new generalization of Apostol type Hermite-Genocchi polynomials and its applications

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Araci S., Khan W. A., AÇIKGÖZ M., Ozel C., Kumam P.

SPRINGERPLUS, cilt.5, 2016 (SCI-Expanded) identifier identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 5
  • Basım Tarihi: 2016
  • Doi Numarası: 10.1186/s40064-016-2357-4
  • Dergi Adı: SPRINGERPLUS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Anahtar Kelimeler: Hermite polynomials, Genocchi polynomials, Hermite-Genocchi polynomials, Apostol-Genocchi polynomials, Summation formulae, Symmetric identities, IMPLICIT SUMMATION FORMULAS, SYMMETRIC IDENTITIES, EULER POLYNOMIALS, BERNOULLI, EXTENSIONS, NUMBERS
  • Dokuz Eylül Üniversitesi Adresli: Evet

Özet

By using the modified Milne-Thomson's polynomial given in Araci et al. (Appl Math Inf Sci 8(6):2803-2808, 2014), we introduce a new concept of the Apostol Hermite-Genocchi polynomials. We also perform a further investigation for aforementioned polynomial and derive some implicit summation formulae and general symmetric identities arising from different analytical means and generating functions method. The results obtained here are an extension of Hermite-Bernoulli polynomials (Pathan and Khan in Mediterr J Math 12:679-695, 2015a) and Hermite-Euler polynomials (Pathan and Khan in Mediterr J Math 2015b, doi:10.1007/s00009-015-0551-1) to Apostol type Hermite-Genocchi polynomials defined in this paper.