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Question Number 52499 by Joel578 last updated on 09/Jan/19

$$\mathrm{Let}f\mathrm{is}\mathrm{a}{2}^{\mathrm{nd}}\mathrm{degree}\mathrm{polynomial}.$$$$\frac{1}{2\pi i}{\int }_{\mid z\mid =2}\frac{zf{}^{\prime }\left(z\right)}{f\left(z\right)}dz=0,\mathrm{and}\frac{1}{2\pi i}{\int }_{\mid z\mid =2}\frac{z^{2}f{}^{\prime }\left(z\right)}{f\left(z\right)}dz=-2$$$$\mathrm{If}f\left(0\right)=2017,\mathrm{find}\mathrm{explicit}\mathrm{form}\mathrm{of}f\left(z\right)$$

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