ON STARLIKENESS OF REGULAR COULOMB WAVE FUNCTIONS

In this paper, we study some geometric properties of a class of analytic functions which is defined from the J-fraction expansion of the ratio zf'(z)/f(z). We find the disk domain which is mapped into a starlike do-main by these functions. Moreover, we study similar results for two different normalized forms of regular Coulomb wave functions and a normalized Bessel function of the first kind by using continued fractions expansions.

Automated summary

In this paper, we investigate the geometric properties of a certain class of analytic functions obtained from the J-fraction expansion of the ratio zf'(z)/f(z). We establish that these functions map a disk domain to a starlike domain. Furthermore, we extend our study to two different normalized forms of regular Coulomb wave functions and a normalized Bessel function of the first kind using continued fractions expansions.