Define $F(x) = \sum\_{n\geq 1} f\_{n}x^n$ and $G(x) = \sum\_{n\geq 1} g\_{n}x^n$. Then the Hadamard product of $F$ and $G$ is


$$H(x):=(F\*G)(x) = \sum\_{n\geq 1} f\_{n}g\_{n}x^n.$$


The author of [Riesz equivalent of Riemann hypothesis and Hadamard product](https://mathoverflow.net/q/351443) claims that 


$$H(x) = \frac{1}{2\pi}\int\_{0}^{2\pi} F(\sqrt {x} e^{it})G(\sqrt {x} e^{-it}) \mathrm{d}t.$$


However, no reference/proof of this identity was given. So, does anyone know where I can find the proof/reference of this identity ?



Reference request for the integral representation of the Hadamard product of two infinite series
E.C. Titchmarsh, The theory of functions, Oxford University Press


Section 4.6 Hadamard multiplication theorem, p.158


