#include "numeric.h"
#include "power.h"
#include "symbol.h"
+#include "utils.h"
+#ifndef NO_GINAC_NAMESPACE
namespace GiNaC {
+#endif // ndef NO_GINAC_NAMESPACE
//////////
// Riemann's Zeta-function
//////////
-static ex zeta_eval(ex const & x)
+static ex zeta1_evalf(ex const & x)
+{
+ BEGIN_TYPECHECK
+ TYPECHECK(x,numeric)
+ END_TYPECHECK(zeta(x))
+
+ return zeta(ex_to_numeric(x));
+}
+
+static ex zeta1_eval(ex const & x)
{
if (x.info(info_flags::numeric)) {
numeric y = ex_to_numeric(x);
// trap integer arguments:
if (y.is_integer()) {
if (y.is_zero())
- return -exHALF();
- if (!x.compare(exONE()))
+ return -_ex1_2();
+ if (x.is_equal(_ex1()))
throw(std::domain_error("zeta(1): infinity"));
if (x.info(info_flags::posint)) {
if (x.info(info_flags::odd))
return zeta(x).hold();
else
- return abs(bernoulli(y))*pow(Pi,x)*numTWO().power(y-numONE())/factorial(y);
+ return abs(bernoulli(y))*pow(Pi,x)*_num2().power(y-_num1())/factorial(y);
} else {
if (x.info(info_flags::odd))
- return -bernoulli(numONE()-y)/(numONE()-y);
+ return -bernoulli(_num1()-y)/(_num1()-y);
else
- return numZERO();
+ return _num0();
}
}
}
return zeta(x).hold();
}
-static ex zeta_evalf(ex const & x)
+static ex zeta1_diff(ex const & x, unsigned diff_param)
{
- BEGIN_TYPECHECK
- TYPECHECK(x,numeric)
- END_TYPECHECK(zeta(x))
+ GINAC_ASSERT(diff_param==0);
- return zeta(ex_to_numeric(x));
+ return zeta(_ex1(), x);
}
-static ex zeta_diff(ex const & x, unsigned diff_param)
+const unsigned function_index_zeta1 = function::register_new("zeta", zeta1_eval, zeta1_evalf, zeta1_diff, NULL);
+
+//////////
+// Derivatives of Riemann's Zeta-function zeta(0,x)==zeta(x)
+//////////
+
+static ex zeta2_eval(ex const & n, ex const & x)
{
- ASSERT(diff_param==0);
+ if (n.info(info_flags::numeric)) {
+ // zeta(0,x) -> zeta(x)
+ if (n.is_zero())
+ return zeta(x);
+ }
- return exZERO(); // should return zeta(numONE(),x);
+ return zeta(n, x).hold();
}
-static ex zeta_series(ex const & x, symbol const & s, ex const & point, int order)
+static ex zeta2_diff(ex const & n, ex const & x, unsigned diff_param)
{
- throw(std::logic_error("don't know the series expansion of the zeta function"));
+ GINAC_ASSERT(diff_param<2);
+
+ if (diff_param==0) {
+ // d/dn zeta(n,x)
+ throw(std::logic_error("cannot diff zeta(n,x) with respect to n"));
+ }
+ // d/dx psi(n,x)
+ return zeta(n+1,x);
}
-REGISTER_FUNCTION(zeta, zeta_eval, zeta_evalf, zeta_diff, zeta_series);
+const unsigned function_index_zeta2 = function::register_new("zeta", zeta2_eval, NULL, zeta2_diff, NULL);
+#ifndef NO_GINAC_NAMESPACE
} // namespace GiNaC
+#endif // ndef NO_GINAC_NAMESPACE