Fix NaN in th_jac2jac/th_jac2cheb when γ+β+1 == 0 - #271
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e.g. th_jac2cheb(x, -0.25, -0.25) returned NaN in the first entry: the second Toeplitz-dot-Hankel step converts to (-1/2,-1/2) from β = -1/2 so the left diagonal is (2k+λ)Λ(k,λ,μ) with λ = 0, which is 0*Inf at k = 0. Use λΓ(λ) = Γ(λ+1) for that entry. Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
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Fixes NaN in the first row of ChebyshevT() \ Ultraspherical(0.25), which now goes through th_jac2cheb(·, -0.25, -0.25) (JuliaApproximation/FastTransforms.jl#271). Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
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* Add ConnectionMatrix for dense conversions using FastTransforms Conversions between Chebyshev, Legendre, Ultraspherical and Jacobi whose matrices are dense (non-integer parameter differences) now return a ConnectionMatrix. Multiplying or dividing coefficients with finitely many non-zeros applies FastTransforms Toeplitz-dot-Hankel transforms, and finite sections are computed with a single transform. This adds support for ChebyshevT \ Ultraspherical(λ) and Ultraspherical \ Ultraspherical with non-integer differences, and Jacobi \ Jacobi with non-integer differences, which previously threw. In particular findall(iszero, diff(f)) now works for Legendre expansions. Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com> * Add ConnectionMatrix to the docs Fixes the :missing_docs error in the Documentation build. Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com> * improvements * Require FastTransforms 0.17.3 Fixes NaN in the first row of ChebyshevT() \ Ultraspherical(0.25), which now goes through th_jac2cheb(·, -0.25, -0.25) (JuliaApproximation/FastTransforms.jl#271). Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com> * use explicit formulas for getindex * Cover remaining ConnectionMatrix lines in tests Test size/copy, column sections, integer coefficients, a conversion with a negative integer parameter difference and a directly constructed Ultraspherical/Jacobi ConnectionMatrix. Remove two unreachable methods. Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com> --------- Co-authored-by: Claude Opus 5.5 <noreply@anthropic.com>
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th_jac2cheb(x, -0.25, -0.25)(and similar, e.g.th_jac2jac(x, -0.25, -0.25, 0.5, 0.5)) returnedNaNin the first entry for every length.The conversion is split into two Toeplitz-dot-Hankel steps. With
α = β = -0.25,_nearest_jacobi_pargives exactly-1/2for the intermediate parameters. The left diagonal(2k+λ)Λ(k,λ,μ)therefore hasλ = γ+β+1 = 0, so itsk = 0entry is0*Γ(0)/Γ(μ) = 0*Inf. This PR computes that entry asΓ(λ+1)/Γ(μ), usingλΓ(λ) = Γ(λ+1). It is the same value forλ ≠ 0and the correct limit atλ = 0.This shows up in ClassicalOrthogonalPolynomials.jl:
(ChebyshevT() \\ Ultraspherical(0.25))[1:10,1:10]now goes throughth_jac2cheb(·, -0.25, -0.25).The PR adds regression tests and bumps the version to 0.17.3.
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