Starlike Functions Associated with Bernoulli's Numbers of Second Kind

The aim of this paper is to introduce a class of starlike functions that are related to Bernoulli's numbers of the second kind. Let phi(BS) ((zeta) over tilde) = ((zeta) over tilde /e((zeta) over tilde) -1)(2) = Sigma(infinity)(n=0) (zeta) over tilde B-n(n)2 /n! , where the coefficients of B-n(2) are Bernoulli numbers of the second kind. Then, we introduce a subclass of starlike functions F such that (zeta) over tildeF'((zeta) over tilde)/F((zeta) over tilde) (SIC) phi(BS) ((zeta) over tilde). found out the coefficient bounds, several radii problems, structural formulas, and inclusion relations. We also found sharp Hankel determinant problems of this class.

Automated summary

The aim of this paper is to introduce a class of starlike functions related to Bernoulli's numbers of the second kind. We define phi(BS) ((zeta) over tilde) = ((zeta) over tilde /e((zeta) over tilde) -1)(2) = Sigma(infinity)(n=0) (zeta) over tilde B-n(n)2 /n! , where the coefficients of B-n(2) are Bernoulli numbers of the second kind. We then introduce a subclass of starlike functions F such that (zeta) over tildeF'((zeta) over tilde)/F((zeta) over tilde) (SIC) phi(BS) ((zeta) over tilde). We explore coefficient bounds, radii problems, structural formulas, inclusion relations, and sharp Hankel determinant problems of this class.