Escape errors in the latex documentation

src/WilliamsonTransforms.jl

@@ -21,12 +21,12 @@ Computes the Williamson d-transform of the random variable X, taken at point x.
 For a univariate non-negative random variable ``X``, with cumulative distribution function ``F`` and an integer ``d\\ge 2``, the Williamson-d-transform of ``X`` is the real function supported on ``[0,\\infty[`` given by:
 
 ```math
-\phi(t) = 𝒲_{d}(X)(t) = \\int_{t}^{\\infty} \\left(1 - \\frac{t}{x}\\right)^{d-1} dF(x) = \\mathbb E\\left( (1 - \\frac{t}{X})^{d-1}_+\\right) \\mathbb 1_{t > 0} + \\left(1 - F(0)\\right)\\mathbb 1_{t <0}
+\\phi(t) = 𝒲_{d}(X)(t) = \\int_{t}^{\\infty} \\left(1 - \\frac{t}{x}\\right)^{d-1} dF(x) = \\mathbb E\\left( (1 - \\frac{t}{X})^{d-1}_+\\right) \\mathbb 1_{t > 0} + \\left(1 - F(0)\\right)\\mathbb 1_{t <0}
 ```
 
 This function has several properties: 
     - ``\\phi(0) = 1`` and ``\\phi(Inf) = 0``
-    - ``\\phi`` is ``d-2`` times derivable, and the signs of its derivatives alternates : ``\\forall k \\in 0,...,d-2, (-1)^k \phi^{(k)} \\ge 0``.
+    - ``\\phi`` is ``d-2`` times derivable, and the signs of its derivatives alternates : ``\\forall k \\in 0,...,d-2, (-1)^k \\phi^{(k)} \\ge 0``.
     - ``\\phi^{(d-2)}`` is convex.
 
 These properties makes this function what is called an *archimedean generator*, able to generate *archimedean copulas* in dimensions up to ``d``. 
@@ -68,13 +68,13 @@ Computes the inverse Williamson d-transform of the d-monotone archimedean genera
 
 A ``d``-monotone archimedean generator is a function ``\\phi`` on ``\\mathbb R_+`` that has these three properties:
 - ``\\phi(0) = 1`` and ``\\phi(Inf) = 0``
-- ``\\phi`` is ``d-2`` times derivable, and the signs of its derivatives alternates : ``\\forall k \\in 0,...,d-2, (-1)^k \phi^{(k)} \\ge 0``.
+- ``\\phi`` is ``d-2`` times derivable, and the signs of its derivatives alternates : ``\\forall k \\in 0,...,d-2, (-1)^k \\phi^{(k)} \\ge 0``.
 - ``\\phi^{(d-2)}`` is convex.
 
 For such a function ``\\phi``, the inverse Williamson-d-transform of ``\\phi`` is the cumulative distribution function ``F`` of a non-negative random variable ``X``, defined by : 
 
 ```math
-F(x) = 𝒲_{d}^{-1}(\phi)(x) = 1 - \\frac{(-x)^{d-1} \\phi_+^{(d-1)}(x)}{k!} - \\sum_{k=0}^{d-2} \\frac{(-x)^k \\phi^{(k)}(x)}{k!}
+F(x) = 𝒲_{d}^{-1}(\\phi)(x) = 1 - \\frac{(-x)^{d-1} \\phi_+^{(d-1)}(x)}{k!} - \\sum_{k=0}^{d-2} \\frac{(-x)^k \\phi^{(k)}(x)}{k!}
 ```
 
 We return this cumulative distribution function in the form of the corresponding random variable `<:Distributions.ContinuousUnivariateDistribution` from `Distributions.jl`. You may then compute :