63 lines
1.5 KiB
Plaintext
63 lines
1.5 KiB
Plaintext
[/
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Copyright 2019, Nick Thompson
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Distributed under the Boost Software License, Version 1.0.
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(See accompanying file LICENSE_1_0.txt or copy at
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http://www.boost.org/LICENSE_1_0.txt).
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]
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[section:jacobi Jacobi Polynomials]
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[h4 Synopsis]
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``
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#include <boost/math/special_functions/jacobi.hpp>
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``
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namespace boost{ namespace math{
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template<typename Real>
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Real jacobi(unsigned n, Real alpha, Real beta, Real x);
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template<typename Real>
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Real jacobi_derivative(unsigned n, Real alpha, Real beta, Real x, unsigned k);
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template<typename Real>
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Real jacobi_prime(unsigned n, Real alpha, Real beta, Real x);
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template<typename Real>
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Real jacobi_double_prime(unsigned n, Real alpha, Real beta, Real x);
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}} // namespaces
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Jacobi polynomials are a family of orthogonal polynomials.
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A basic usage is as follows:
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using boost::math::jacobi;
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double x = 0.5;
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double alpha = 0.3;
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double beta = 7.2;
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unsigned n = 3;
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double y = jacobi(n, alpha, beta, x);
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All derivatives of the Jacobi polynomials are available.
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The /k/-th derivative of the /n/-th Gegenbauer polynomial is given by
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using boost::math::jacobi_derivative;
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double x = 0.5;
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double alpha = 0.3;
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double beta = 7.2;
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unsigned n = 3;
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double y = jacobi_derivative(n, alpha, beta, x, k);
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For consistency with the rest of the library, `jacobi_prime` is provided which simply returns `jacobi_derivative(n, lambda, x,1)`.
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[$../graphs/jacobi.svg]
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[h3 Implementation]
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The implementation uses the 3-term recurrence for the Jacobi polynomials, rising.
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[endsect]
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