SemiclassicalOrthogonalPolynomials.jl

A Julia repository for semiclassical orthogonal polynomials

This package implements SemiclassicalJacobi, a family of orthogonal polynomials orthogonal with respect to the weight x^a * (1-x)^b * (t-x)^c. This builds on top of ClassicalOrthogonalPolynomials.jl and usage is similar.

For example, the following gives a half-range Chebyshev polynomial:

julia> using SemiclassicalOrthogonalPolynomials
julia> T = SemiclassicalJacobi(2, -1/2, 0, -1/2)
SemiclassicalJacobi with weight x^-0.5 * (1-x)^0.0 * (2.0-x)^-0.5 on 0..1

julia> T[0.1,1:10] # evaluate first 10 OPs at 0.1
10-element Array{Float64,1}:
  1.0
 -0.855801766003832
  0.19083013661761547
  0.5574589013555691
 -1.085921276099753
  1.181713489691121
 -0.8056271765695796
  0.10748539771183807
  0.6338334369113602
 -1.1219700834800677

julia> U = SemiclassicalJacobi(2, 1/2, 0, 1/2, T) # last argument reuses computation from T
SemiclassicalJacobi with weight x^0.5 * (1-x)^0.0 * (2.0-x)^0.5 on 0..1