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README.md

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The function `newtoniansquare([x,y], p)` computes a matrix of Newtonian potentials of Legendre polynomials on the unit square $Ω := [-1,1]^2$. That is it computes
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```math
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\begin{pmatrix}
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L_{11}(𝐱) & \cdots & L_{1,p-1}(𝐱) & L_{1p}(𝐱) \\
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L_{21}(𝐱) & \cdots & L_{2,p-1}(𝐱) \\
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\vdots & \iddots \\
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L_{11}(𝐱) & & L_{1,p-1}(𝐱) & L_{1p}(𝐱) \\
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L_{21}(𝐱) & & L_{2,p-1}(𝐱) \\
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& \\
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L_{p1}(𝐱)
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\end{pmatrix}
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```
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where $𝐱 = [x,y]$ is any point in $ℝ²$ (including on or near the unit square $Ω$) and
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```math
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L_{k,j}(𝐱) := ∬_Ω P_{k-1}(s) P_{j-1}(t) \log(\| [s,t] - [x,y] \|) \, ds \, dt
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L_{k,j}(𝐱) := ∬_Ω P_{k-1}(s) P_{j-1}(t) \log(\| [s,t] - 𝐱 \|) \, ds \, dt
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```
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where $P_k$ and $P_j$ are the Legendre polynomials of degree $k$ and $j$, respectively.
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Here we show an example of how to use the package for computing the Newtonian potential for $f(x,y) = \cos(x*\exp(y))$,
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Here we show an example of how to use the package for computing the Newtonian potential for $f(x,y) = \cos(x \exp(y))$,
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which is faster than QuadGK.jl:
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```julia
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julia> using MultivariateSingularIntegrals, ClassicalOrthogonalPolynomials, LinearAlgebra, QuadGK

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