X-Git-Url: https://www.ginac.de/ginac.git//ginac.git?p=ginac.git;a=blobdiff_plain;f=ginac%2Finifcns_zeta.cpp;h=365f35e22aeb9501541b8fb559a9d44168d171c0;hp=d4890f2863c28205e64931f50e7f2b5074f8239d;hb=69cf20e8ee183eadfe457af33dc88a9f568038e8;hpb=68c28e9c4381f874acf0cd7a690d36098ac9db23

diff --git a/ginac/inifcns_zeta.cpp b/ginac/inifcns_zeta.cpp
index d4890f28..365f35e2 100644
--- a/ginac/inifcns_zeta.cpp
+++ b/ginac/inifcns_zeta.cpp
@@ -3,7 +3,7 @@
  *  Implementation of the Zeta-function and some related stuff. */
 
 /*
- *  GiNaC Copyright (C) 1999 Johannes Gutenberg University Mainz, Germany
+ *  GiNaC Copyright (C) 1999-2003 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
@@ -24,11 +24,12 @@
 #include <stdexcept>
 
 #include "inifcns.h"
-#include "ex.h"
 #include "constant.h"
 #include "numeric.h"
 #include "power.h"
 #include "symbol.h"
+#include "operators.h"
+#include "utils.h"
 
 namespace GiNaC {
 
@@ -36,42 +37,93 @@ namespace GiNaC {
 // Riemann's Zeta-function
 //////////
 
-static ex zeta_eval(ex const & x)
+static ex zeta1_evalf(const ex & x)
 {
-    if (x.info(info_flags::numeric)) {
-        // trap integer arguments:
-        if ( x.info(info_flags::integer) ) {
-            if ( x.info(info_flags::posint) ) {
-                return numZERO();  // FIXME
-            } else {
-                return numZERO();  // FIXME
-            }
-        }
-    }
-    return zeta(x).hold();
-}    
-    
-static ex zeta_evalf(ex const & x)
+	if (is_exactly_a<numeric>(x)) {
+		try {
+			return zeta(ex_to<numeric>(x));
+		} catch (const dunno &e) { }
+	}
+	
+	return zeta(x).hold();
+}
+
+static ex zeta1_eval(const ex & x)
+{
+	if (x.info(info_flags::numeric)) {
+		const numeric &y = ex_to<numeric>(x);
+		// trap integer arguments:
+		if (y.is_integer()) {
+			if (y.is_zero())
+				return _ex_1_2;
+			if (y.is_equal(_num1))
+				throw(std::domain_error("zeta(1): infinity"));
+			if (y.info(info_flags::posint)) {
+				if (y.info(info_flags::odd))
+					return zeta(x).hold();
+				else
+					return abs(bernoulli(y))*pow(Pi,y)*pow(_num2,y-_num1)/factorial(y);
+			} else {
+				if (y.info(info_flags::odd))
+					return -bernoulli(_num1-y)/(_num1-y);
+				else
+					return _ex0;
+			}
+		}
+		// zeta(float)
+		if (y.info(info_flags::numeric) && !y.info(info_flags::crational))
+			return zeta1_evalf(x);
+	}
+	return zeta(x).hold();
+}
+
+static ex zeta1_deriv(const ex & x, unsigned deriv_param)
 {
-    BEGIN_TYPECHECK
-        TYPECHECK(x,numeric)
-    END_TYPECHECK(zeta(x))
-    
-    return zeta(ex_to_numeric(x));
+	GINAC_ASSERT(deriv_param==0);
+	
+	return zeta(_ex1, x);
 }
 
-static ex zeta_diff(ex const & x, unsigned diff_param)
+unsigned zeta1_SERIAL::serial =
+	function::register_new(function_options("zeta").
+	                       eval_func(zeta1_eval).
+	                       evalf_func(zeta1_evalf).
+	                       derivative_func(zeta1_deriv).
+	                       latex_name("\\zeta").
+	                       overloaded(2));
+
+//////////
+// Derivatives of Riemann's Zeta-function  zeta(0,x)==zeta(x)
+//////////
+
+static ex zeta2_eval(const ex & n, const ex & x)
 {
-    ASSERT(diff_param==0);
-    
-    return exZERO();  // should return zeta(numONE(),x);
+	if (n.info(info_flags::numeric)) {
+		// zeta(0,x) -> zeta(x)
+		if (n.is_zero())
+			return zeta(x);
+	}
+	
+	return zeta(n, x).hold();
 }
 
-static ex zeta_series(ex const & x, symbol const & s, ex const & point, int order)
+static ex zeta2_deriv(const ex & n, const ex & x, unsigned deriv_param)
 {
-    throw(std::logic_error("don't know the series expansion of the zeta function"));
+	GINAC_ASSERT(deriv_param<2);
+	
+	if (deriv_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);
+unsigned zeta2_SERIAL::serial =
+	function::register_new(function_options("zeta").
+	                       eval_func(zeta2_eval).
+	                       derivative_func(zeta2_deriv).
+	                       latex_name("\\zeta").
+	                       overloaded(2));
 
 } // namespace GiNaC