/usr/include/legendre.h is in libalglib-dev 2.6.0-3.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
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>>> SOURCE LICENSE >>>
This program is free software; you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation (www.fsf.org); either version 2 of the
License, or (at your option) any later version.
This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
A copy of the GNU General Public License is available at
http://www.fsf.org/licensing/licenses
>>> END OF LICENSE >>>
*************************************************************************/
#ifndef _legendre_h
#define _legendre_h
#include "ap.h"
#include "ialglib.h"
/*************************************************************************
Calculation of the value of the Legendre polynomial Pn.
Parameters:
n - degree, n>=0
x - argument
Result:
the value of the Legendre polynomial Pn at x
*************************************************************************/
double legendrecalculate(const int& n, const double& x);
/*************************************************************************
Summation of Legendre polynomials using Clenshaw�s recurrence formula.
This routine calculates
c[0]*P0(x) + c[1]*P1(x) + ... + c[N]*PN(x)
Parameters:
n - degree, n>=0
x - argument
Result:
the value of the Legendre polynomial at x
*************************************************************************/
double legendresum(const ap::real_1d_array& c, const int& n, const double& x);
/*************************************************************************
Representation of Pn as C[0] + C[1]*X + ... + C[N]*X^N
Input parameters:
N - polynomial degree, n>=0
Output parameters:
C - coefficients
*************************************************************************/
void legendrecoefficients(const int& n, ap::real_1d_array& c);
#endif
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