Higher order generalized geometric polynomials


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KARGIN L., ÇEKİM B.

TURKISH JOURNAL OF MATHEMATICS, vol.42, no.3, pp.887-903, 2018 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 42 Issue: 3
  • Publication Date: 2018
  • Doi Number: 10.3906/mat-1705-95
  • Journal Name: TURKISH JOURNAL OF MATHEMATICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, TR DİZİN (ULAKBİM)
  • Page Numbers: pp.887-903
  • Keywords: Generalized geometric polynomials, Bernoulli polynomials, Euler polynomials, Riemann zeta function, R-WHITNEY NUMBERS, BERNOULLI, FORMULA, SUMS, CONNECTION, SERIES
  • Akdeniz University Affiliated: Yes

Abstract

According to the generalized Mellin derivative, we introduce a new family of polynomials called higher order generalized geometric polynomials and obtain some arithmetical properties of them. Then we investigate the relationship of these polynomials with degenerate Bernoulli, degenerate Euler, and Bernoulli polynomials. Finally, we evaluate several series and integrals in closed forms.