+/** Gamma-function. */
+DECLARE_FUNCTION_1P(lgamma)
+DECLARE_FUNCTION_1P(tgamma)
+
+/** Beta-function. */
+DECLARE_FUNCTION_2P(beta)
+
+// overloading at work: we cannot use the macros here
+/** Psi-function (aka digamma-function). */
+class psi1_SERIAL { public: static unsigned serial; };
+template<typename T1>
+inline function psi(const T1 & p1) {
+ return function(psi1_SERIAL::serial, ex(p1));
+}
+/** Derivatives of Psi-function (aka polygamma-functions). */
+class psi2_SERIAL { public: static unsigned serial; };
+template<typename T1, typename T2>
+inline function psi(const T1 & p1, const T2 & p2) {
+ return function(psi2_SERIAL::serial, ex(p1), ex(p2));
+}
+class psi_SERIAL;
+template<> inline bool is_the_function<class psi_SERIAL>(const ex & x)
+{
+ return is_the_function<psi1_SERIAL>(x) || is_the_function<psi2_SERIAL>(x);
+}
+