# User:Jan Homann/Mathematics

**Mathematics**

**Polynomial Functions**

**Roots**

**Rational Functions**

**Exp, Gauss**

**Sin, Cos, Tan, Cot, Sec, Csc**

**Sinh, Cosh, Tanh, Coth, Sech, Csch**

**ArcSin, ArcCos, ArcTan, ArcCot, ArcSec, ArcCsc**

**ArcSinh, ArcCosh, ArcTanh, ArcCoth, ArcSech, ArcCsch**

**Log, ProductLog**

**PolyLog**

**Gamma, Reciprocal Gamma**

**LogGamma, Polygammas**

**Riemann Siegel Theta (in 3 different magnifications), Riemann Siegel Z (in 2 different magnifications)**

**Riemann zeta, Dirichlet eta, Riemann Xi **

**Eisenstein series**

**KleinInvariantJ, Modular lambda, Dedekind eta **

**Theta**

**Zeros of Riemann zeta function**

I used Mathematica 5.0 to generate the plots. I do not know how to add the corresponding Mathematica worksheet here. Therefore I took a screenshot of it for now, to make it possible for other people to reproduce the results. The color mapping is designed such that the phase of a complex number is always visible, even if the complex number approaches an absolute values of zero or infinity. You are welcome to generate further graphs. Please add the color map to the graph's description page! Please let me know about new graphs on my wikipedia user page Jan Homann!

There is a very nice version of the function for Mathematica 6.0 which you can directly download here [[1]]

Functions can show line-artefacts. To counter this, slightly expand the picture in the mathematica worksheet.