What is implemented?
Mathematica in Education and Research 6, n4, 27 (1997)
Mathematica in Education and Research forthcoming (2000)
results partially published in the Wolfram Research Poster Series and notebooks from
www.specialfunctions.com and The Mathematica GuideBook (forthcoming)
When is a representation faithful?
- Polynomial case: Re or Im
- General case: more complicated
Implicitly defined functions that can't be solved for .
- (Lambert/ProductLog function)
- (Kepler equation, ε a numeric parameter)
- (eigenvalue equation of a square well)
- (eigenvalue equation delta function potential)
- Solve numerically transcendental equations in a
The special functions of mathematical physics.
- Again solving odes around branch points
- Use functional relations
- Problem for some functions: new
branch points at nonprincipal sheets
Riemann surfaces of special functions
Other visualization techniques
- Interactive cuts with projections through 4D --space
- Spheres with ears
Riemann surfaces over the Riemann sphere
Animations of Riemann Surfaces with Movable Branch Points
Click on one one of the below equations to see the succession of images that compromise the notebook animation.