Exact Results in Quantum Theory

Certain classical special functions can be expressed by Rodrigues' type formulas, such as the Jacobi polynomials, generalized Laguerre polynomials, and Hermite polynomials (do not forget the most important example: monomials with negative powers.). In this talk, we will explore the common topological nature behind these formulas. Various orthogonal properties will become direct consequences from this viewpoint.