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Question Number 151065 by qaz last updated on 18/Aug/21

$$\mathrm{Calculate}::{\int }_{-\mathrm{\infty }}^{+\mathrm{\infty }}\frac{\mathrm{\Gamma }\left(\mathrm{x}\right)}{\mathrm{\Gamma }(\mathrm{x}+\mathrm{a})}\sin \left(\pi \mathrm{x}\right)\mathrm{dx}=\frac{2^{\mathrm{a}-1}}{\mathrm{\Gamma }\left(\mathrm{a}\right)}\pi (\mathrm{a}>0)$$

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