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.
Generalized geometric polynomials, Bernoulli polynomials, Euler polynomials, Riemann zeta function
KARGIN, LEVENT and ÇEKİM, BAYRAM
"Higher order generalized geometric polynomials,"
Turkish Journal of Mathematics: Vol. 42:
3, Article 13.
Available at: https://journals.tubitak.gov.tr/math/vol42/iss3/13