Chebyshev Quadrature

Author

Eric W. Weisstein
December 24, 2006

This notebook downloaded from http://mathworld.wolfram.com/notebooks/NumericalMath/ChebyshevQuadrature.nb.

For more information, see Eric's MathWorld entry http://mathworld.wolfram.com/ChebyshevQuadrature.html.

©2006 Wolfram Research, Inc. except for portions noted otherwise

Table

Table[Together//@ChebyshevQuadratureExact[i],{i,2,5}]//TableForm

%//N//TableForm

Polynomials

s[n_,y_]:=Series[Exp[(1/2)n(-2+Log[1-y](1-(1/y))+Log[1+y](1+(1/y)))],{y,0,n}]//Normal

<<DiscreteMath`RSolve`

SeriesTerm[Exp[(1/2)n(-2+Log[1-y](1-(1/y))+Log[1+y](1+(1/y)))],{y,0,n}]

SeriesTerm[Exp[(1/2)n(-2+Log[1-y](1-(1/y))+Log[1+y](1+(1/y)))],{y,∞,n}]

SeriesCoefficient[Exp[(1/2)n(-2+Log[1-y](1-(1/y))+Log[1+y](1+(1/y)))],{y,0,n}]

SeriesCoefficient[Exp[(1/2)n(-2+Log[1-y](1-(1/y))+Log[1+y](1+(1/y)))],{y,∞,n}]

G[n_,x_]:=Factor[(x^n)s[n,y]/.y->1/x]

Table[G[n,x],{n,0,9}]//TableForm//TraditionalForm