Questions tagged [polylogarithm]
For questions about or related to polylogarithm functions.
546
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A new proof a non-linear Euler sum
According to Nielsen we have the following :
If $$f(x)= \sum_{n\geq 0}a_n x^n $$
Then we have the following
$$\tag{1}\int^1_0 f(xt)\, \mathrm{Li}_2(t)\, dx=\frac{\pi^2}{6x}\int^x_0 f(t)\, dt
-\...
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Short calculation of the dilogarithm?
Is there a nice way to implement the dilogarithm function for real values, without actually performing the integration?
A series solution would have been nice, but the series around $0$ has a ...
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The most complete reference for identities and special values for polylogarithm and polygamma functions
I am looking for a book, paper, web site, etc. (or several ones) containing the most complete list of identities and special values for the polylogarithm $\operatorname{Li}_s(z)$ and polygamma $\psi^{(...
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Indefinite integral $\int \arcsin \left(k\sin x\right) dx$
It would take too long to explain the context reasonably well - but in short, this integral, or rather its equivalent
$$\int\frac{x\cos x\,dx}{\sqrt{1-k^2\sin^2x}},\qquad 0<k<1$$
is related to ...
- 53.4k
15
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Simplification of a trilogarithm of a complex argument
Is it possible to simplify the following expression?
$$\large\Im\,\operatorname{Li}_3\left(-e^{\xi\,\left(\sqrt3-\sqrt{-1}\right)-\frac{\pi^2}{12\,\xi}\left(\sqrt3+\sqrt{-1}\right)}\right)$$
where
$$\...
- 53.4k
0
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How to plot (y vs x) a not invertible function say F(x,y)=const?
I am trying to plot (y vs x) for a not invertible function PolyLogarithm[1.5,y/x]=const.
Any Ideas how to do this, say on Mathematica?
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