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Question Number 110954 by mathmax by abdo last updated on 01/Sep/20

verify the formulae  Σ_(n=−∞) ^(+∞)  (1/((na +1)^p )) =−(π/a^n ) lim_(z→−(1/a))    (1/((p−1)!)){cotan(πz)}^((p−1))   inthis case  1)  a =1 and p=2  2) a=2   and p=2  3)a=2 and p=3  4) a=3 and p=2

$$\mathrm{verify}\:\mathrm{the}\:\mathrm{formulae} \\ $$$$\sum_{\mathrm{n}=−\infty} ^{+\infty} \:\frac{\mathrm{1}}{\left(\mathrm{na}\:+\mathrm{1}\right)^{\mathrm{p}} }\:=−\frac{\pi}{\mathrm{a}^{\mathrm{n}} }\:\mathrm{lim}_{\mathrm{z}\rightarrow−\frac{\mathrm{1}}{\mathrm{a}}} \:\:\:\frac{\mathrm{1}}{\left(\mathrm{p}−\mathrm{1}\right)!}\left\{\mathrm{cotan}\left(\pi\mathrm{z}\right)\right\}^{\left(\mathrm{p}−\mathrm{1}\right)} \\ $$$$\left.\mathrm{inthis}\:\mathrm{case}\:\:\mathrm{1}\right)\:\:\mathrm{a}\:=\mathrm{1}\:\mathrm{and}\:\mathrm{p}=\mathrm{2} \\ $$$$\left.\mathrm{2}\right)\:\mathrm{a}=\mathrm{2}\:\:\:\mathrm{and}\:\mathrm{p}=\mathrm{2} \\ $$$$\left.\mathrm{3}\right)\mathrm{a}=\mathrm{2}\:\mathrm{and}\:\mathrm{p}=\mathrm{3} \\ $$$$\left.\mathrm{4}\right)\:\mathrm{a}=\mathrm{3}\:\mathrm{and}\:\mathrm{p}=\mathrm{2} \\ $$

Answered by mathmax by abdo last updated on 01/Sep/20

sorry −(π/a^p )

$$\mathrm{sorry}\:−\frac{\pi}{\mathrm{a}^{\mathrm{p}} } \\ $$

Commented by khaki last updated on 01/Sep/20

please solve one quation evaluate the integral. ax+b/ax2+bx+c

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