* some related stuff. */
/*
- * GiNaC Copyright (C) 1999-2003 Johannes Gutenberg University Mainz, Germany
+ * GiNaC Copyright (C) 1999-2005 Johannes Gutenberg University Mainz, Germany
*
* 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
*
* You should have received a copy of the GNU General Public License
* along with this program; if not, write to the Free Software
- * Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
+ * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
*/
#include <vector>
{
if (x.info(info_flags::numeric)) {
// trap integer arguments:
- const numeric two_x = _num2*ex_to<numeric>(x);
+ const numeric two_x = (*_num2_p)*ex_to<numeric>(x);
if (two_x.is_even()) {
// tgamma(n) -> (n-1)! for postitive n
if (two_x.is_positive()) {
- return factorial(ex_to<numeric>(x).sub(_num1));
+ return factorial(ex_to<numeric>(x).sub(*_num1_p));
} else {
throw (pole_error("tgamma_eval(): simple pole",1));
}
// trap positive x==(n+1/2)
// tgamma(n+1/2) -> Pi^(1/2)*(1*3*..*(2*n-1))/(2^n)
if (two_x.is_positive()) {
- const numeric n = ex_to<numeric>(x).sub(_num1_2);
- return (doublefactorial(n.mul(_num2).sub(_num1)).div(pow(_num2,n))) * sqrt(Pi);
+ const numeric n = ex_to<numeric>(x).sub(*_num1_2_p);
+ return (doublefactorial(n.mul(*_num2_p).sub(*_num1_p)).div(pow(*_num2_p,n))) * sqrt(Pi);
} else {
// trap negative x==(-n+1/2)
// tgamma(-n+1/2) -> Pi^(1/2)*(-2)^n/(1*3*..*(2*n-1))
- const numeric n = abs(ex_to<numeric>(x).sub(_num1_2));
- return (pow(_num_2, n).div(doublefactorial(n.mul(_num2).sub(_num1))))*sqrt(Pi);
+ const numeric n = abs(ex_to<numeric>(x).sub(*_num1_2_p));
+ return (pow(*_num_2_p, n).div(doublefactorial(n.mul(*_num2_p).sub(*_num1_p))))*sqrt(Pi);
}
}
// tgamma_evalf should be called here once it becomes available
// tgamma(x) == tgamma(x+1) / x
// from which follows
// series(tgamma(x),x==-m,order) ==
- // series(tgamma(x+m+1)/(x*(x+1)*...*(x+m)),x==-m,order+1);
+ // series(tgamma(x+m+1)/(x*(x+1)*...*(x+m)),x==-m,order);
const ex arg_pt = arg.subs(rel, subs_options::no_pattern);
if (!arg_pt.info(info_flags::integer) || arg_pt.info(info_flags::positive))
throw do_taylor(); // caught by function::series()
ex ser_denom = _ex1;
for (numeric p; p<=m; ++p)
ser_denom *= arg+p;
- return (tgamma(arg+m+_ex1)/ser_denom).series(rel, order+1, options);
+ return (tgamma(arg+m+_ex1)/ser_denom).series(rel, order, options);
}
ny.is_real() && ny.is_integer()) {
if (nx.is_negative()) {
if (nx<=-ny)
- return pow(_num_1, ny)*beta(1-x-y, y);
+ return pow(*_num_1_p, ny)*beta(1-x-y, y);
else
throw (pole_error("beta_eval(): simple pole",1));
}
if (ny.is_negative()) {
if (ny<=-nx)
- return pow(_num_1, nx)*beta(1-y-x, x);
+ return pow(*_num_1_p, nx)*beta(1-y-x, x);
else
throw (pole_error("beta_eval(): simple pole",1));
}
throw do_taylor(); // caught by function::series()
// trap the case where arg1 is on a pole:
if (arg1.info(info_flags::integer) && !arg1.info(info_flags::positive))
- arg1_ser = tgamma(arg1+s).series(rel, order, options);
+ arg1_ser = tgamma(arg1+s);
else
- arg1_ser = tgamma(arg1).series(rel,order);
+ arg1_ser = tgamma(arg1);
// trap the case where arg2 is on a pole:
if (arg2.info(info_flags::integer) && !arg2.info(info_flags::positive))
- arg2_ser = tgamma(arg2+s).series(rel, order, options);
+ arg2_ser = tgamma(arg2+s);
else
- arg2_ser = tgamma(arg2).series(rel,order);
+ arg2_ser = tgamma(arg2);
// trap the case where arg1+arg2 is on a pole:
if ((arg1+arg2).info(info_flags::integer) && !(arg1+arg2).info(info_flags::positive))
- arg1arg2_ser = tgamma(arg2+arg1+s).series(rel, order, options);
+ arg1arg2_ser = tgamma(arg2+arg1+s);
else
- arg1arg2_ser = tgamma(arg2+arg1).series(rel,order);
+ arg1arg2_ser = tgamma(arg2+arg1);
// compose the result (expanding all the terms):
return (arg1_ser*arg2_ser/arg1arg2_ser).series(rel, order, options).expand();
}
if (nx.is_positive()) {
// psi(n) -> 1 + 1/2 +...+ 1/(n-1) - Euler
numeric rat = 0;
- for (numeric i(nx+_num_1); i>0; --i)
+ for (numeric i(nx+(*_num_1_p)); i>0; --i)
rat += i.inverse();
return rat-Euler;
} else {
throw (pole_error("psi_eval(): simple pole",1));
}
}
- if ((_num2*nx).is_integer()) {
+ if (((*_num2_p)*nx).is_integer()) {
// half integer case
if (nx.is_positive()) {
// psi((2m+1)/2) -> 2/(2m+1) + 2/2m +...+ 2/1 - Euler - 2log(2)
numeric rat = 0;
- for (numeric i = (nx+_num_1)*_num2; i>0; i-=_num2)
- rat += _num2*i.inverse();
+ for (numeric i = (nx+(*_num_1_p))*(*_num2_p); i>0; i-=(*_num2_p))
+ rat += (*_num2_p)*i.inverse();
return rat-Euler-_ex2*log(_ex2);
} else {
// use the recurrence relation
// where r == ((-1/2)^(-1) + ... + (-m-1/2)^(-1))
numeric recur = 0;
for (numeric p = nx; p<0; ++p)
- recur -= pow(p, _num_1);
+ recur -= pow(p, *_num_1_p);
return recur+psi(_ex1_2);
}
}
}
unsigned psi1_SERIAL::serial =
- function::register_new(function_options("psi").
+ function::register_new(function_options("psi", 1).
eval_func(psi1_eval).
evalf_func(psi1_evalf).
derivative_func(psi1_deriv).
const numeric &nx = ex_to<numeric>(x);
if (nx.is_integer()) {
// integer case
- if (nx.is_equal(_num1))
+ if (nx.is_equal(*_num1_p))
// use psi(n,1) == (-)^(n+1) * n! * zeta(n+1)
- return pow(_num_1,nn+_num1)*factorial(nn)*zeta(ex(nn+_num1));
+ return pow(*_num_1_p,nn+(*_num1_p))*factorial(nn)*zeta(ex(nn+(*_num1_p)));
if (nx.is_positive()) {
// use the recurrence relation
// psi(n,m) == psi(n,m+1) - (-)^n * n! / m^(n+1)
// where r == (-)^n * n! * (1^(-n-1) + ... + (m-1)^(-n-1))
numeric recur = 0;
for (numeric p = 1; p<nx; ++p)
- recur += pow(p, -nn+_num_1);
- recur *= factorial(nn)*pow(_num_1, nn);
+ recur += pow(p, -nn+(*_num_1_p));
+ recur *= factorial(nn)*pow((*_num_1_p), nn);
return recur+psi(n,_ex1);
} else {
// for non-positive integers there is a pole:
throw (pole_error("psi2_eval(): pole",1));
}
}
- if ((_num2*nx).is_integer()) {
+ if (((*_num2_p)*nx).is_integer()) {
// half integer case
- if (nx.is_equal(_num1_2))
+ if (nx.is_equal(*_num1_2_p))
// use psi(n,1/2) == (-)^(n+1) * n! * (2^(n+1)-1) * zeta(n+1)
- return pow(_num_1,nn+_num1)*factorial(nn)*(pow(_num2,nn+_num1) + _num_1)*zeta(ex(nn+_num1));
+ return pow(*_num_1_p,nn+(*_num1_p))*factorial(nn)*(pow(*_num2_p,nn+(*_num1_p)) + (*_num_1_p))*zeta(ex(nn+(*_num1_p)));
if (nx.is_positive()) {
- const numeric m = nx - _num1_2;
+ const numeric m = nx - (*_num1_2_p);
// use the multiplication formula
// psi(n,2*m) == (psi(n,m) + psi(n,m+1/2)) / 2^(n+1)
// to revert to positive integer case
- return psi(n,_num2*m)*pow(_num2,nn+_num1)-psi(n,m);
+ return psi(n,(*_num2_p)*m)*pow((*_num2_p),nn+(*_num1_p))-psi(n,m);
} else {
// use the recurrence relation
// psi(n,-m-1/2) == psi(n,-m-1/2+1) - (-)^n * n! / (-m-1/2)^(n+1)
// where r == (-)^(n+1) * n! * ((-1/2)^(-n-1) + ... + (-m-1/2)^(-n-1))
numeric recur = 0;
for (numeric p = nx; p<0; ++p)
- recur += pow(p, -nn+_num_1);
- recur *= factorial(nn)*pow(_num_1, nn+_num_1);
+ recur += pow(p, -nn+(*_num_1_p));
+ recur *= factorial(nn)*pow(*_num_1_p, nn+(*_num_1_p));
return recur+psi(n,_ex1_2);
}
}
}
unsigned psi2_SERIAL::serial =
- function::register_new(function_options("psi").
+ function::register_new(function_options("psi", 2).
eval_func(psi2_eval).
evalf_func(psi2_evalf).
derivative_func(psi2_deriv).
git://www.ginac.de / ginac.git / blobdiff