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+[section:trigamma Trigamma]
+
+[h4 Synopsis]
+
+``
+#include <boost/math/special_functions/trigamma.hpp>
+``
+
+  namespace boost{ namespace math{
+  
+  template <class T>
+  ``__sf_result`` trigamma(T z);
+  
+  template <class T, class ``__Policy``>
+  ``__sf_result`` trigamma(T z, const ``__Policy``&);
+  
+  }} // namespaces
+  
+[h4 Description]
+
+Returns the trigamma function of /x/. Trigamma is defined as the 
+derivative of the digamma function:
+
+[equation trigamma1]
+
+[graph trigamma]
+
+[optional_policy]
+
+The return type of this function is computed using the __arg_pomotion_rules:
+the result is of type `double` when T is an integer type, and type T otherwise.
+
+[h4 Accuracy]
+
+The following table shows the peak errors (in units of epsilon) 
+found on various platforms with various floating point types.
+Unless otherwise specified any floating point type that is narrower
+than the one shown will have __zero_error.
+
+[table
+[[Significand Size] [Platform and Compiler] [Random Values] ]
+[[53]            [Win32 Visual C++ 12]  [Peak=1.0 Mean=0.4] ]
+[[64]            [Win64 Mingw GCC]  [Peak=1.4 Mean=0.4]  ]
+[[113]           [Win64 Mingw GCC __float128]    [Peak=1.0 Mean=0.5] ]
+]
+
+As shown above, error rates are generally very low for built in types.
+For multiprecision types, error rates are typically in the order of a
+few epsilon.
+
+[h4 Testing]
+
+Testing is against Mathematica generated spot values to 35 digit precision.
+
+[h4 Implementation]
+
+The arbitrary precision version of this function simply calls __polygamma.
+
+For built in fixed precision types, negative arguments are first made positive via:
+
+[equation trigamma2]
+
+Then arguments in the range \[0, 1) are shifted to >= 1 via:
+
+[equation trigamma3]
+
+Then evaluation is via one of a number of rational approximations, for small x these are
+of the form:
+
+[equation trigamma4]
+
+and for large x of the form:
+
+[equation trigamma5]
+
+[endsect][/section:digamma The Trigamma Function]
+
+[/ 
+  Copyright 2014 John Maddock and Paul A. Bristow.
+  Distributed under 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).
+]
+