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Results tagged with integration
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user 51143
Questions related to various forms of integration including the Riemann integral, Lebesgue integral, Riemann–Stieltjes integral, double integrals, line integrals, contour integrals, surface integrals, integrals of differential forms, ...
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How do I Calculate :$\int_{0}^{1}x^{k}\psi(x)dx$ where $k\geq 3$ is an integer?
How do I Calculate, if possible, in terms of well-known constants the integral :
$\int_{0}^{1}x^{k}\psi(x)dx$ , where $k\geq 3$ is an integer ?
note: $\psi(x)$ is digamma function.
Any help would b …
- 83
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How do I Calculate :$\int_{0}^{1}x^{k}\psi(x)dx$ where $k\geq 3$ is an integer?
Hint :
I think this is a closed form of :$\int_{0}^{1}x^{k}\psi(x)dx$ for $ k>2$:
for $ k>2 $:
$\int_{0}^{1}x^{k}\psi(x)dx$=$-log\sqrt{2\pi} +\sum_{j=1}^{k-1}(-1)^{j+1}C_{k}^{j}logA_{j}$
where :$A …
- 83