/usr/include/psif.h is in libalglib-dev 2.6.0-3.
This file is owned by root:root, with mode 0o644.
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Cephes Math Library Release 2.8: June, 2000
Copyright by Stephen L. Moshier
Contributors:
* Sergey Bochkanov (ALGLIB project). Translation from C to
pseudocode.
See subroutines comments for additional copyrights.
>>> 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
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>>> END OF LICENSE >>>
*************************************************************************/
#ifndef _psif_h
#define _psif_h
#include "ap.h"
#include "ialglib.h"
/*************************************************************************
Psi (digamma) function
d -
psi(x) = -- ln | (x)
dx
is the logarithmic derivative of the gamma function.
For integer x,
n-1
-
psi(n) = -EUL + > 1/k.
-
k=1
This formula is used for 0 < n <= 10. If x is negative, it
is transformed to a positive argument by the reflection
formula psi(1-x) = psi(x) + pi cot(pi x).
For general positive x, the argument is made greater than 10
using the recurrence psi(x+1) = psi(x) + 1/x.
Then the following asymptotic expansion is applied:
inf. B
- 2k
psi(x) = log(x) - 1/2x - > -------
- 2k
k=1 2k x
where the B2k are Bernoulli numbers.
ACCURACY:
Relative error (except absolute when |psi| < 1):
arithmetic domain # trials peak rms
IEEE 0,30 30000 1.3e-15 1.4e-16
IEEE -30,0 40000 1.5e-15 2.2e-16
Cephes Math Library Release 2.8: June, 2000
Copyright 1984, 1987, 1992, 2000 by Stephen L. Moshier
*************************************************************************/
double psi(double x);
#endif
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