some more doc fixes

Author: MikaelSlevinsky

src/GramMatrix.jl

@@ -11,7 +11,7 @@ Construct a symmetric positive-definite Gram matrix with data stored in ``W``.
 Given a family of orthogonal polynomials ``𝐏(x) = {p₀(x), p₁(x),…}``
 and a continuous inner product ``⟨f, g⟩``, the Gram matrix is defined by:
 ```math
-Wᵢⱼ = ⟨pᵢ₋₁, pⱼ₋₁⟩.
+W[i, j] = ⟨pᵢ₋₁, pⱼ₋₁⟩.
 ```
 Moreover, given ``X``, the transposed Jacobi matrix that satisfies ``x 𝐏(x) = 𝐏(x) X``,
 the Gram matrix satisfies the skew-symmetric rank-2 displacement equation (``X = X[1:n, 1:n]``):
@@ -20,7 +20,7 @@ XᵀW - WX = GJGᵀ,
 ```
 where ``J = [0 1; -1 0]`` and where:
 ```math
-G[:, 1] = 𝐞_n, G_{:, 2} = W[n-1, :]X[n-1, n] - Xᵀ W[:, n].
+G[:, 1] = 𝐞ₙ, \\quad  G[:, 2] = W[n-1, :]X[n-1, n] - Xᵀ W[:, n].
 ```
 Fast (``O(n^2)``) Cholesky factorization of the Gram matrix returns the
 connection coefficients between ``𝐏(x)`` and the polynomials ``𝐐(x)``
@@ -54,8 +54,8 @@ GramMatrix(W::WT, X::XT) where {T, WT <: AbstractMatrix{T}, XT <: AbstractMatrix
     GramMatrix(μ::AbstractVector, X::AbstractMatrix)
 
 Construct a GramMatrix from modified orthogonal polynomial moments and the multiplication operator.
-In the standard (classical) normalization, ``p_0(x) = 1``, so that the moments
-``µ_n = ⟨ p_{n-1}, 1⟩`` are in fact the first column of the Gram matrix.
+In the standard (classical) normalization, ``p₀(x) = 1``, so that the moments
+``µ[n] = ⟨ pₙ₋₁, 1⟩`` are in fact the first column of the Gram matrix.
 The recurrence is built from ``XᵀW = WX``.
 """
 GramMatrix(μ::AbstractVector{T}, X::XT) where {T, XT <: AbstractMatrix{T}} = GramMatrix(μ, X, one(T))
@@ -221,12 +221,12 @@ end
 
 Construct a Chebyshev--Gram matrix of size `(length(μ)+1)÷2` with entries:
 ```math
-W_{i,j} = \\frac{µ_{|i-j|+1} +µ_{i+j-1}}{2}.
+2 W[i, j] = µ_{|i-j|+1} + µ_{i+j-1}.
 ```
 Due to the linearization of a product of two first-kind Chebyshev polynomials,
 the Chebyshev--Gram matrix can be constructed from modified Chebyshev moments:
 ```math
-µ_{n} = ⟨ T_{n-1}, 1⟩.
+µ[n] = ⟨ Tₙ₋₁, 1⟩.
 ```
 Specialized construction and Cholesky factorization is given for this type.