Revision as of 20:27, 25 June 2017

The dilogarithm function $\mathrm{Li}_2$ is defined for $|z| \leq 1$ by $$\mathrm{Li}_2(z)=\displaystyle\sum_{k=1}^{\infty} \dfrac{z^k}{k^2},$$ which is a special case of the polylogarithm.

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)
Li2(z)=zPhi(z,2,1)

References

• 1953: Harry Bateman: Higher Transcendental Functions Volume I ... (previous) ... (next): $\S 1.11.1 (22)$
• 1958: Leonard Lewin: Dilogarithms and Associated Functions ... (next): $(1.1)$
• 1981: Leonard Lewin: Polylogarithms and Associated Functions (2nd ed.) ... (next): $(1.1)$
• 1991: Leonard Lewin: Structural Properties of Polylogarithms ... (next): $(1.1)$

(page 31)
The Dilogarithm function
[1]

Dilogarithm

Log integral

Logarithm

Polylogarithm