diff --git a/kmplot/parser.h b/kmplot/parser.h
--- a/kmplot/parser.h
+++ b/kmplot/parser.h
@@ -85,7 +85,7 @@
 
 
 const int legendreCount = 7; // number of legendre polynomials we allow for
-const int ScalarCount = 40+legendreCount;	// number of mathematical scalar functions
+const int ScalarCount = 41+legendreCount;	// number of mathematical scalar functions
 const int VectorCount = 3; // number of vector functions
 //@}
 
@@ -125,6 +125,9 @@
 double legendre5(double x);
 double legendre6(double x);
 
+double evaluate_rational(const double* num, const double* denom, const double& z_, int count);
+double besselj0(double x);
+
 double factorial(double x);
 double lerf(double x);
 double lerfc(double x);
diff --git a/kmplot/parser.cpp b/kmplot/parser.cpp
--- a/kmplot/parser.cpp
+++ b/kmplot/parser.cpp
@@ -44,6 +44,7 @@
 #include <math.h>
 #include <assert.h>
 #include <cmath>
+#include <tr1/cmath>
 #include <limits>
 #include <locale.h>
 
@@ -115,6 +116,9 @@
 	{"P_4", QString(), legendre4},				// lengedre polynomial (n=4)
 	{"P_5", QString(), legendre5},				// lengedre polynomial (n=5)
 	{"P_6", QString(), legendre6},				// lengedre polynomial (n=6)
+	
+	// bessel
+	{"J0", QString(), besselj0},				// the cylindrical Bessel function of the first kind (n=0)
 };
 
 VectorFunction Parser::vectorFunctions[ VectorCount ]=
@@ -1395,6 +1399,165 @@
 	return (231*x*x*x*x*x*x - 315*x*x*x*x + 105*x*x - 5)/16;
 }
 
+//  The following function code is adopted from Boost.
+//  Use, modification and distribution are subject to the
+//  Boost Software License, Version 1.0. (See accompanying file
+//  LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+
+double evaluate_rational(const double* num, const double* denom, const double& x_, int count)
+{
+   double x(x_);
+   double s1, s2;
+   if (x <= 1)
+   {
+      s1 = num[count-1];
+      s2 = denom[count-1];
+      for (int i = count - 2; i >= 0; --i)
+      {
+         s1 *= x;
+         s2 *= x;
+         s1 += num[i];
+         s2 += denom[i];
+      }
+   }
+   else
+   {
+      x = 1 / x;
+      s1 = num[0];
+      s2 = denom[0];
+      for(unsigned i = 1; i < (unsigned)count; ++i)
+      {
+         s1 *= x;
+         s2 *= x;
+         s1 += num[i];
+         s2 += denom[i];
+      }
+   }
+   return s1 / s2;
+}
+
+//  The following function code is adopted from Boost.
+//  Use, modification and distribution are subject to the
+//  Boost Software License, Version 1.0. (See accompanying file
+//  LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+
+double besselj0( double x ) {
+    static const double P1[] = {
+         -4.1298668500990866786e+11,
+         2.7282507878605942706e+10,
+         -6.2140700423540120665e+08,
+         6.6302997904833794242e+06,
+         -3.6629814655107086448e+04,
+         1.0344222815443188943e+02,
+         -1.2117036164593528341e-01
+    };
+    static const double Q1[] = {
+         2.3883787996332290397e+12,
+         2.6328198300859648632e+10,
+         1.3985097372263433271e+08,
+         4.5612696224219938200e+05,
+         9.3614022392337710626e+02,
+         1.0,
+         0.0
+    };
+    static const double P2[] = {
+         -1.8319397969392084011e+03,
+         -1.2254078161378989535e+04,
+         -7.2879702464464618998e+03,
+         1.0341910641583726701e+04,
+         1.1725046279757103576e+04,
+         4.4176707025325087628e+03,
+         7.4321196680624245801e+02,
+         4.8591703355916499363e+01
+    };
+    static const double Q2[] = {
+         -3.5783478026152301072e+05,
+         2.4599102262586308984e+05,
+         -8.4055062591169562211e+04,
+         1.8680990008359188352e+04,
+         -2.9458766545509337327e+03,
+         3.3307310774649071172e+02,
+         -2.5258076240801555057e+01,
+         1.0
+    };
+    static const double PC[] = {
+         2.2779090197304684302e+04,
+         4.1345386639580765797e+04,
+         2.1170523380864944322e+04,
+         3.4806486443249270347e+03,
+         1.5376201909008354296e+02,
+         8.8961548424210455236e-01
+    };
+    static const double QC[] = {
+         2.2779090197304684318e+04,
+         4.1370412495510416640e+04,
+         2.1215350561880115730e+04,
+         3.5028735138235608207e+03,
+         1.5711159858080893649e+02,
+         1.0
+    };
+    static const double PS[] = {
+        -8.9226600200800094098e+01,
+        -1.8591953644342993800e+02,
+        -1.1183429920482737611e+02,
+        -2.2300261666214198472e+01,
+        -1.2441026745835638459e+00,
+        -8.8033303048680751817e-03
+    };
+    static const double QS[] = {
+         5.7105024128512061905e+03,
+         1.1951131543434613647e+04,
+         7.2642780169211018836e+03,
+         1.4887231232283756582e+03,
+         9.0593769594993125859e+01,
+         1.0
+    };
+    static const double x1  =  2.4048255576957727686e+00,
+                   x2  =  5.5200781102863106496e+00,
+                   x11 =  6.160e+02,
+                   x12 =  -1.42444230422723137837e-03,
+                   x21 =  1.4130e+03,
+                   x22 =  5.46860286310649596604e-04;
+
+    double value, factor, r, rc, rs;
+
+    if (x < 0)
+    {
+        x = -x;                         // even function
+    }
+    if (x == 0)
+    {
+        return 1;
+    }
+    if (x <= 4)                       // x in (0, 4]
+    {
+        double y = x * x;
+        r = evaluate_rational(P1, Q1, y, 7);
+        factor = (x + x1) * ((x - x11/256) - x12);
+        value = factor * r;
+    }
+    else if (x <= 8.0)                  // x in (4, 8]
+    {
+        double y = 1 - (x * x)/64;
+        r = evaluate_rational(P2, Q2, y, 8);
+        factor = (x + x2) * ((x - x21/256) - x22);
+        value = factor * r;
+    }
+    else                                // x in (8, \infty)
+    {
+        double y = 8 / x;
+        double y2 = y * y;
+        rc = evaluate_rational(PC, QC, y2, 6);
+        rs = evaluate_rational(PS, QS, y2, 6);
+        factor = 1/ sqrt(M_PI) / sqrt(x);
+        double sx = sin(x);
+        double cx = cos(x);
+        value = factor * (rc * (cx + sx) - y * rs * (sx - cx));
+    }
+
+    return value;
+}
+
 double sign(double x)
 {
 	if(x<0.)