All Questions
5
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Relations between Dilogarithms and Imaginary part of Hurwitz-Zeta function
I'm working through a paper that involves a problem concerning the calculation of the Imaginary part of the derivative of the Hurwitz-Zeta function $\zeta_H(z,a)$ with respect to $z$, evaluated at a ...
1
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1
answer
59
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Connection between the polylogarithm and the Bernoulli polynomials.
I have been studying the polylogarithm function and came across its relation with Bernoulli polynomials, as Wikipedia site asserts:
For positive integer polylogarithm orders $s$, the Hurwitz zeta ...
- 812
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59
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Difference of polylogarithms of complex conjugate arguments
I have the expression
$$\tag{1}
\operatorname{Li}_{1/2}(z)-\operatorname{Li}_{1/2}(z^*)
$$
Where $\operatorname{Li}$ is the polylogarithm and $^*$ denotes complex conjugation. The expression is ...
- 4,817
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Patterns for the polylogarithm $\rm{Li}_m\big(\tfrac12\big)$ and Nielsen polylogarithm $S_{n,p}\big(\tfrac12\big)$?
The polylogarithm $\rm{Li}_m\big(\tfrac12\big)$ has closed-forms known for $m=1,2,3$. It seems this triad pattern extends to the Nielsen generalized logarithm $S_{n,p}\,\big(\tfrac12\big)$ for $n=0,1,...
- 54.9k
8
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Why does the tribonacci constant have a trilogarithm ladder?
When I came across the dilogarithm ladders of Coxeter and Landen, namely,
$$\text{Li}_2\Big(\frac1{\phi^6}\Big)-4\text{Li}_2\Big(\frac1{\phi^3}\Big)-3\text{Li}_2\Big(\frac1{\phi^2}\Big)+6\text{Li}_2\...
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