Constrained coefficients problem for generalized typically real functions

For let denote the class of generalized typically real functions i.e. the class of functions of a formwhere , and is the unique probability measure on the interval . For the same range of parameters, let the generalized Chebyshev polynomials of the second kind be defined as followsWe see thatThe main purpose of a paper is a solution of coefficients problems in . Problem related to the well-known Zalcman conjecture is presented.