Event Date
2000-11-29
Event Time
12:10 pm ~ 01:00 pm
Event Location
Student Lounge
The first set of interesting functions we meet in mathematics (after polynomials) are circular functions $\sin x$ and $\cos x$. They are related to the circle group and to the ordinary differential operator $\frac{d^2}{dx^2}+1$, which is a polynomial in $\frac{d}{dx}$ with constant coefficients. The next in this hierarchy is the class of hypergeometric functions. They are solutions of the equation of the form \[P_1(\frac{d}{dx})=xP_2(\frac{d}{dx}),\] where $P_1$ and $P_2$ are polynomials in $\frac{d}{dx}$ with constant coefficients. The simple factor $x$ makes a world of a difference. In particular it changes the abelian group (circle group) into a non-abelian group.