fix chebyshev derivative (#407)

Author: jverzani

src/polynomials/ChebyshevT.jl

@@ -185,7 +185,7 @@ function derivative(p::ChebyshevT{T}, order::Integer = 1) where {T}
     n = length(p)
     der = Vector{R}(undef, n)
 
-    for j in n:-1:2
+    for j in n:-1:3
         der[j] = 2j * q[j]
         q[j - 2] += j * q[j] / (j - 2)
     end

test/ChebyshevT.jl

@@ -199,6 +199,12 @@ end
         @test degree(truncate(p - integrate(derivative(p)), atol=1e-8)) <= 0
         @test degree(truncate(p - derivative(integrate(p)), atol=1e-8)) <= 0
     end
+
+    ## issue SpeicalPolynomials #56
+    coeffs  = [3 // 4, -2 // 1, 1 // 1]
+    p = ChebyshevT(coeffs)
+    @test derivative(p) ≈ convert(ChebyshevT, derivative(convert(Polynomial, p)))
+    @test derivative(p, 2) ≈ convert(ChebyshevT, derivative(convert(Polynomial, p), 2))
 end
 
 @testset "z-series" for i in 0:5