Let $h:[0,2\pi]\to [a,b]$ be a continuous function of bounded variation and let $$f(z)=exp\left[\dfrac{1}{2\pi}\int\limits_0^{2\pi}\dfrac{e^{it}+z}{e^{it}-z}h(t)dt\right].$$ Can we say that Taylor coefficients of under bracket function are the Fourier coefficients of $h$?
Thanks in advance.