Polynomial Conjecture : Let w(x) denote a function that is positive a. e. on an interval (a, b) CR,
and assume that the moments Mr = 4 w(x) =* dx exists and are finite for all NonNegative integers k.
Let {Pm} m, denote the sequence of orthogonal polynomials, with Pm(x) of degree m in x, i. e.,
w(x) Pm(x) Pn(x) dx-com. ng
where c>0 and where om, denotes the Kronecker delta. If for m > 1, Pm(x) = 0 for x = x. M<...<XN,
with m-M+N+1, and if the numbers Bft are defined by
Pm(x)
W(x)
dx,
(x - xz) P(x)
Pn(x)
Box- S
W(x)
dx,
(x -xx) P.,(xx)