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FunctionIntegrator.md

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@@ -44,7 +44,7 @@ julia> using FunctionIntegrator
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## Choice of function
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As a general rule of thumb, `adaptive_simpsons_rule` should be the function you use when you are unsure which function to use, as its accuracy is more predictable. The main time when `adaptive_simpsons_rule` should be avoided is when there are unremovable singularities at the endpoints of the domain of integration, in which case using `chebyshev_quadrature` with $k=1$ or using `legendre_quadrature` is likely best.
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Each of the functions whose name ends with `_quadrature` uses [Gaussian quadrature](https://en.wikipedia.org/wiki/Gaussian_quadrature) is the specifics of which differ between functions. Out of them, `legendre_quadrature` is perhaps the best to go with when you are uncertain which out of the `_quadrature` functions to go with as it can be applied to any grid and any problem and *usually* arrives at a result that is accurate to at least 7 decimal places provided $N \geq 1 \times 10^{4}$. `legendre_quadrature` has the added benefit of being perhaps the fastest `_quadrature` function after controlling for accuracy of the result obtained.
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Each of the functions whose name ends with `_quadrature` uses [Gaussian quadrature](https://en.wikipedia.org/wiki/Gaussian_quadrature), the specifics of which differ between functions. Out of them, `legendre_quadrature` is perhaps the best to go with when you are uncertain which out of the `_quadrature` functions to go with as it can be applied to any grid and any problem and *usually* arrives at a result that is accurate to at least seven significant figures provided $N \geq 1 \times 10^{4}$. `legendre_quadrature` has the added benefit of being perhaps the fastest `_quadrature` function after controlling for accuracy of the result obtained.
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The [test/](https://github.com/fusion809/FunctionIntegrator.jl/tree/master/test/) folder has test scripts that approximate various different integrals (each file, except [test/runtests.jl](https://github.com/fusion809/FunctionIntegrator.jl/blob/master/test/runtests.jl), pertains to a different integral); the N values given are the smallest possible to pass each of the tests listed (except when the test involves a less than (<) sign). If you want to know which function to use for which integral is these tests may be useful as a rough guide.
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