update beta error messages and checks (#1003)

Author: ryanelandt

include/boost/math/special_functions/beta.hpp

@@ -1021,18 +1021,15 @@ T ibeta_imp(T a, T b, T x, const Policy& pol, bool inv, bool normalised, T* p_de
    BOOST_MATH_ASSERT((p_derivative == 0) || normalised);
 
    if(!(boost::math::isfinite)(a))
-      return policies::raise_domain_error<T>(function, "The argument a to the incomplete beta function must be >= zero (got a=%1%).", a, pol);
+      return policies::raise_domain_error<T>(function, "The argument a to the incomplete beta function must be finite (got a=%1%).", a, pol);
    if(!(boost::math::isfinite)(b))
-      return policies::raise_domain_error<T>(function, "The argument b to the incomplete beta function must be >= zero (got b=%1%).", b, pol);
-   if(!(boost::math::isfinite)(x))
+      return policies::raise_domain_error<T>(function, "The argument b to the incomplete beta function must be finite (got b=%1%).", b, pol);
+   if (!(0 <= x && x <= 1))
       return policies::raise_domain_error<T>(function, "The argument x to the incomplete beta function must be in [0,1] (got x=%1%).", x, pol);
 
    if(p_derivative)
       *p_derivative = -1; // value not set.
 
-   if((x < 0) || (x > 1))
-      return policies::raise_domain_error<T>(function, "Parameter x outside the range [0,1] in the incomplete beta function (got x=%1%).", x, pol);
-
    if(normalised)
    {
       if(a < 0)
@@ -1422,18 +1419,16 @@ T ibeta_derivative_imp(T a, T b, T x, const Policy& pol)
    // start with the usual error checks:
    //
    if (!(boost::math::isfinite)(a))
-      return policies::raise_domain_error<T>(function, "The argument a to the incomplete beta function must be >= zero (got a=%1%).", a, pol);
+      return policies::raise_domain_error<T>(function, "The argument a to the incomplete beta function must be finite (got a=%1%).", a, pol);
    if (!(boost::math::isfinite)(b))
-      return policies::raise_domain_error<T>(function, "The argument b to the incomplete beta function must be >= zero (got b=%1%).", b, pol);
-   if (!(boost::math::isfinite)(x))
+      return policies::raise_domain_error<T>(function, "The argument b to the incomplete beta function must be finite (got b=%1%).", b, pol);
+   if (!(0 <= x && x <= 1))
       return policies::raise_domain_error<T>(function, "The argument x to the incomplete beta function must be in [0,1] (got x=%1%).", x, pol);
 
    if(a <= 0)
       return policies::raise_domain_error<T>(function, "The argument a to the incomplete beta function must be greater than zero (got a=%1%).", a, pol);
    if(b <= 0)
       return policies::raise_domain_error<T>(function, "The argument b to the incomplete beta function must be greater than zero (got b=%1%).", b, pol);
-   if((x < 0) || (x > 1))
-      return policies::raise_domain_error<T>(function, "Parameter x outside the range [0,1] in the incomplete beta function (got x=%1%).", x, pol);
    //
    // Now the corner cases:
    //