Category:Spence's Function
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This category contains results about Spence's Function.
Definitions specific to this category can be found in Definitions/Spence's Function.
Spence's function is a special case of the polylogarithm, defined for $z \in \C$ by the integral:
- $\ds \map {\Li_2} z = -\int_0^z \frac {\map \Ln {1 - t} } t \rd t$
where:
- $\ds \int_0^z$ is an integral across the straight line in the complex plane connecting $0$ and $z$
- $\Ln$ is the principal branch of the complex natural logarithm.
Subcategories
This category has the following 2 subcategories, out of 2 total.
D
- Dilogarithm of Square (3 P)
E
Pages in category "Spence's Function"
The following 16 pages are in this category, out of 16 total.
D
- Definite Integral from 0 to 1 of Zeta of 2 minus Dilogarithm of x over One minus x
- Definite Integral over Unit Square of Logarithm of x minus Logarithm of y over x minus y
- Dilogarithm Function/Examples
- Dilogarithm of Minus Golden Mean
- Dilogarithm of Minus One
- Dilogarithm of Minus Reciprocal of Golden Mean
- Dilogarithm of Minus Z Plus Dilogarithm of Minus Reciprocal of Z
- Dilogarithm of One
- Dilogarithm of One Half
- Dilogarithm of One Minus Reciprocal of Golden Mean
- Dilogarithm of One Minus Z Plus Dilogarithm of One Minus Reciprocal of Z
- Dilogarithm of Reciprocal of Golden Mean
- Dilogarithm of Square
- Dilogarithm of Zero
- Dilogarithm Reflection Formula