Formula:DLMF:25.12:E15

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formula in Polylogarithms

Formula:DLMF:25.12:E16:SE1 >>

${\displaystyle{\displaystyle{\displaystyle G_{s}(x)=\frac{1}{\Gamma\left(s+1\right)}\int_{0}^{\infty}\frac{t^{s}}{{\mathrm{e}^{t-x}}-1}\mathrm{d}t}}}$

Constraint(s)

${\displaystyle{\displaystyle{\displaystyle s>-1}}}$, ${\displaystyle{\displaystyle{\displaystyle x<0}}}$, or ${\displaystyle{\displaystyle{\displaystyle s>0}}}$, ${\displaystyle{\displaystyle{\displaystyle x\leq 0}}}$

Name

Bose-Einstein integral

Proof

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Symbols List

${\displaystyle{\displaystyle{\displaystyle\Gamma}}}$ : Euler's gamma function : http://dlmf.nist.gov/5.2#E1
${\displaystyle{\displaystyle{\displaystyle\int}}}$ : integral : http://dlmf.nist.gov/1.4#iv
${\displaystyle{\displaystyle{\displaystyle\mathrm{e}}}}$ : the base of the natural logarithm : http://dlmf.nist.gov/4.2.E11
${\displaystyle{\displaystyle{\displaystyle\mathrm{d}^{n}x}}}$ : differential : http://dlmf.nist.gov/1.4#iv

Bibliography

Equation (15), Section 25.12 of DLMF.

URL links

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