Heine–Stieltjes polynomials
In mathematics, the Heine–Stieltjes polynomials or Stieltjes polynomials, introduced by, are polynomial solutions of a second-order Fuchsian equation, a differential equation all of whose singularities are regular. The Fuchsian equation has the form
for some polynomial V of degree at most N − 2, and if this has a polynomial solution S then V is called a Van Vleck polynomial and S is called a Heine–Stieltjes polynomial.
Heun polynomials are the special cases of Stieltjes polynomials when the differential equation has four singular points.
