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* refactor gaussjacobi

* fix typo in the document

* fix airy_roots and add doctests in constants.jl

* refactor gausshermite

* use CAPITAL_CASE for global constants

* fix typo

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A Julia package to compute n-point Gauss quadrature nodes and weights to 16-digit accuracy and in O(n) time. So far the package includes gausschebyshev(), gausslegendre(), gaussjacobi(), gaussradau(), gausslobatto(), gausslaguerre(), and gausshermite(). This package is heavily influenced by Chebfun.

An introduction to Gauss quadrature can be found here. For a quirky account on the history of computing Gauss-Legendre quadrature, see [6].

Our Aims

  • The fastest Julia code for Gauss quadrature nodes and weights (without tabulation).
  • Change the perception that Gauss quadrature rules are expensive to compute.

Example usage

julia> @time nodes, weights = gausslegendre( 100000 );
  0.002192 seconds (10 allocations: 2.289 MiB)

# integrates f(x) = x^2 from -1 to 1
julia> @time dot( weights, nodes.^2 )
  0.000184 seconds (7 allocations: 781.422 KiB)