Out of curiosity: Is there a nice integral representation of Clausen function of order $2n$? $\mathrm{Cl}_{2n}(x)$
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@ClaudeLeibovici I think it's only for $\mathrm{Cl}_2(x)$? – BooleanCoder Apr 24 '21 at 06:40
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$\operatorname{Cl}{2n}(x)$ is a polylogarithm in disguise, with many known integral representations. Say, $$\operatorname{Cl}{2n}(x)=\frac{\sin x}{2(2n-1)!}\int_0^\infty\frac{y^{2n-1},dy}{\cosh y-\cos x}.$$ – metamorphy Apr 24 '21 at 07:30
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@metamorphy Can you please tell sources for it's integral representations? – BooleanCoder Apr 24 '21 at 07:32
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Wikipedia and the links out there. – metamorphy Apr 24 '21 at 07:37
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@metamorphy Any idea for $\mathrm{Cl}_{2n+1}(x)$? – BooleanCoder Apr 24 '21 at 07:38
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1$$\operatorname{Cl}{2n+1}(x)=\frac1{2(2n)!}\int_0^\infty y^{2n}\frac{\cos x-e^{-y}}{\cosh y-\cos x},dy$$ is obtained the same way as for $\operatorname{Cl}{2n}(x)$. – metamorphy Apr 24 '21 at 07:46