*
* Implementation of Gamma function and some related stuff. */
+/*
+ * GiNaC Copyright (C) 1999 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
+ * the Free Software Foundation; 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.
+ *
+ * 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
+ */
+
#include <vector>
#include <stdexcept>
-#include "ginac.h"
+#include "inifcns.h"
+#include "ex.h"
+#include "constant.h"
+#include "numeric.h"
+#include "power.h"
+#include "symbol.h"
+
+namespace GiNaC {
//////////
// gamma function
* evaluation some day...
*
* @exception fail_numeric("complex_infinity") or something similar... */
-ex gamma_eval(ex const & x)
+static ex gamma_eval(ex const & x)
{
- if ( x.info(info_flags::numeric) ) {
+ if (x.info(info_flags::numeric)) {
// trap integer arguments:
if ( x.info(info_flags::integer) ) {
numeric n = ex_to_numeric(x).sub(numHALF());
numeric coefficient = doublefactorial(n.mul(numTWO()).sub(numONE()));
coefficient = coefficient.div(numTWO().power(n));
- return mul(coefficient,power(Pi,numHALF()));
+ return coefficient * pow(Pi,numHALF());
} else {
// trap negative x=(-n+1/2)
// gamma(-n+1/2) -> Pi^(1/2)*(-2)^n/(1*3*..*(2*n-1))
numeric n = abs(ex_to_numeric(x).sub(numHALF()));
numeric coefficient = numeric(-2).power(n);
coefficient = coefficient.div(doublefactorial(n.mul(numTWO()).sub(numONE())));;
- return mul(coefficient,power(Pi,numHALF()));
+ return coefficient*sqrt(Pi);
}
}
}
return gamma(x).hold();
}
-ex gamma_evalf(ex const & x)
+static ex gamma_evalf(ex const & x)
{
BEGIN_TYPECHECK
TYPECHECK(x,numeric)
return gamma(ex_to_numeric(x));
}
-ex gamma_diff(ex const & x, unsigned diff_param)
+static ex gamma_diff(ex const & x, unsigned diff_param)
{
ASSERT(diff_param==0);
- return power(x, -1); //!!
+ return psi(exZERO(),x)*gamma(x);
}
-ex gamma_series(ex const & x, symbol const & s, ex const & point, int order)
+static ex gamma_series(ex const & x, symbol const & s, ex const & point, int order)
{
- //!! Only handle one special case for now...
+ // FIXME: Only handle one special case for now...
if (x.is_equal(s) && point.is_zero()) {
- ex e = 1 / s - EulerGamma + s * (power(Pi, 2) / 12 + power(EulerGamma, 2) / 2) + Order(power(s, 2));
+ ex e = 1 / s - EulerGamma + s * (pow(Pi, 2) / 12 + pow(EulerGamma, 2) / 2) + Order(pow(s, 2));
return e.series(s, point, order);
} else
throw(std::logic_error("don't know the series expansion of this particular gamma function"));
}
REGISTER_FUNCTION(gamma, gamma_eval, gamma_evalf, gamma_diff, gamma_series);
+
+//////////
+// psi function (aka polygamma function)
+//////////
+
+/** Evaluation of polygamma-function psi(n,x).
+ * Somebody ought to provide some good numerical evaluation some day... */
+static ex psi_eval(ex const & n, ex const & x)
+{
+ if (n.info(info_flags::numeric) && x.info(info_flags::numeric)) {
+ // do some stuff...
+ }
+ return psi(n, x).hold();
+}
+
+static ex psi_evalf(ex const & n, ex const & x)
+{
+ BEGIN_TYPECHECK
+ TYPECHECK(n,numeric)
+ TYPECHECK(x,numeric)
+ END_TYPECHECK(psi(n,x))
+
+ return psi(ex_to_numeric(n), ex_to_numeric(x));
+}
+
+static ex psi_diff(ex const & n, ex const & x, unsigned diff_param)
+{
+ ASSERT(diff_param==0);
+
+ return psi(n+1, x);
+}
+
+static ex psi_series(ex const & n, ex const & x, symbol const & s, ex const & point, int order)
+{
+ throw(std::logic_error("Nobody told me how to series expand the psi function. :-("));
+}
+
+REGISTER_FUNCTION(psi, psi_eval, psi_evalf, psi_diff, psi_series);
+
+} // namespace GiNaC