On the definition of a close-to-convex function

A. W. Goodman, E. B. Saff
1978 International Journal of Mathematics and Mathematical Sciences  
The standard definition of a close-to-convex function involves a complex numerical factoreiβwhich is on occasion erroneously replaced by1. While it is known to experts in the field that this replacement cannot be made without essentially changing the class, explicit reasons for this fact seem to be lacking in the literature. Our purpose is to fill this gap, and in so doing we are lead to a new coefficient problem which is solved forn=2, but is open forn>2.
doi:10.1155/s0161171278000150 fatcat:sdgpfnmm65aszmxskx4i2viesy