Difference between revisions of "Dilogarithm"
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The dilogarithm function $\mathrm{Li}_2$ is defined for $|z| \leq 1$ by | The dilogarithm function $\mathrm{Li}_2$ is defined for $|z| \leq 1$ by | ||
| − | $$\mathrm{Li}_2(z)=\displaystyle\sum_{k=1}^{\infty} \dfrac{z^k}{k^2} | + | $$\mathrm{Li}_2(z)=\displaystyle\sum_{k=1}^{\infty} \dfrac{z^k}{k^2}, \quad |z| \leq 1,$$ |
which is a special case of the [[polylogarithm]]. | which is a special case of the [[polylogarithm]]. | ||
Revision as of 07:14, 4 June 2016
The dilogarithm function $\mathrm{Li}_2$ is defined for $|z| \leq 1$ by $$\mathrm{Li}_2(z)=\displaystyle\sum_{k=1}^{\infty} \dfrac{z^k}{k^2}, \quad |z| \leq 1,$$ which is a special case of the polylogarithm.
Domain coloring of $\mathrm{Li}_2$.
Properties
Relationship between dilogarithm and log(1-z)/z
Relationship between Li 2(1),Li 2(-1), and pi
Li 2(1)=pi^2/6
Relationship between Li 2(-1/x),Li 2(-x),Li 2(-1), and log^2(x)
Derivative of Li 2(-1/x)
References
- 1926: Leonard Lewin: Polylogarithms and Associated Functions (2nd ed.) ... (next): (1.1)
