Improve doc of special math functions

4 files changed, 51 insertions, 12 deletions

diff --git a/Eigen/src/Core/GlobalFunctions.h b/Eigen/src/Core/GlobalFunctions.h
index 2173e026d..c7d73ff66 100644
--- a/Eigen/src/Core/GlobalFunctions.h
+++ b/Eigen/src/Core/GlobalFunctions.h
@@ -117,8 +117,8 @@ namespace Eigen
   }
   
   /**
-  * \brief Component-wise division of a scalar by array elements.
-  **/
+    * \brief Component-wise division of a scalar by array elements.
+    **/
   template <typename Derived>
   inline const Eigen::CwiseUnaryOp<Eigen::internal::scalar_inverse_mult_op<typename Derived::Scalar>, const Derived>
     operator/(const typename Derived::Scalar& s, const Eigen::ArrayBase<Derived>& a)
@@ -129,10 +129,15 @@ namespace Eigen
     );
   }
 
-  /** \returns an expression of the coefficient-wise igamma(\a a, \a x) to the given arrays.
+  /** \cpp11 \returns an expression of the coefficient-wise igamma(\a a, \a x) to the given arrays.
     *
     * This function computes the coefficient-wise incomplete gamma function.
     *
+    * \note This function supports only float and double scalar types in c++11 mode. To support other scalar types,
+    * or float/double in non c++11 mode, the user has to provide implementations of igammac(T,T) for any scalar
+    * type T to be supported.
+    *
+    * \sa Eigen::igammac(), Eigen::lgamma()
     */
   template<typename Derived,typename ExponentDerived>
   inline const Eigen::CwiseBinaryOp<Eigen::internal::scalar_igamma_op<typename Derived::Scalar>, const Derived, const ExponentDerived>
@@ -144,10 +149,15 @@ namespace Eigen
     );
   }
 
-  /** \returns an expression of the coefficient-wise igammac(\a a, \a x) to the given arrays.
+  /** \cpp11 \returns an expression of the coefficient-wise igammac(\a a, \a x) to the given arrays.
     *
     * This function computes the coefficient-wise complementary incomplete gamma function.
     *
+    * \note This function supports only float and double scalar types in c++11 mode. To support other scalar types,
+    * or float/double in non c++11 mode, the user has to provide implementations of igammac(T,T) for any scalar
+    * type T to be supported.
+    *
+    * \sa Eigen::igamma(), Eigen::lgamma()
     */
   template<typename Derived,typename ExponentDerived>
   inline const Eigen::CwiseBinaryOp<Eigen::internal::scalar_igammac_op<typename Derived::Scalar>, const Derived, const ExponentDerived>
@@ -163,6 +173,11 @@ namespace Eigen
     *
     * It returns the \a n -th derivative of the digamma(psi) evaluated at \c x.
     *
+    * \note This function supports only float and double scalar types in c++11 mode. To support other scalar types,
+    * or float/double in non c++11 mode, the user has to provide implementations of polygamma(T,T) for any scalar
+    * type T to be supported.
+    *
+    * \sa Eigen::digamma()
     */
   // * \warning Be careful with the order of the parameters: x.polygamma(n) is equivalent to polygamma(n,x)
   // * \sa ArrayBase::polygamma()
@@ -183,6 +198,9 @@ namespace Eigen
     * \param x is the exposent, it must be > 1
     * \param q is the shift, it must be > 0
     *
+    * \note This function supports only float and double scalar types. To support other scalar types, the user has
+    * to provide implementations of zeta(T,T) for any scalar type T to be supported.
+    *
     * \sa ArrayBase::zeta()
     */
   template<typename DerivedX,typename DerivedQ>
diff --git a/Eigen/src/Core/SpecialFunctions.h b/Eigen/src/Core/SpecialFunctions.h
index 38debb4d1..4cf58c510 100644
--- a/Eigen/src/Core/SpecialFunctions.h
+++ b/Eigen/src/Core/SpecialFunctions.h
@@ -755,9 +755,9 @@ struct igamma_impl {
 
 #endif  // EIGEN_HAS_C99_MATH
 
-/****************************************************************************
- * Implementation of Riemann zeta function of two arguments                 *
- ****************************************************************************/
+/*****************************************************************************
+ * Implementation of Riemann zeta function of two arguments, based on Cephes *
+ *****************************************************************************/
 
 template <typename Scalar>
 struct zeta_retval {
diff --git a/Eigen/src/plugins/ArrayCwiseBinaryOps.h b/Eigen/src/plugins/ArrayCwiseBinaryOps.h
index 99f4048d7..c3f8c2575 100644
--- a/Eigen/src/plugins/ArrayCwiseBinaryOps.h
+++ b/Eigen/src/plugins/ArrayCwiseBinaryOps.h
@@ -317,13 +317,18 @@ polygamma(const EIGEN_CURRENT_STORAGE_BASE_CLASS<DerivedN> &n) const
 }
 #endif
 
-/** \cpp11 \returns an expression of the coefficient-wise zeta function.
+/** \returns an expression of the coefficient-wise zeta function.
   *
   * It returns the Riemann zeta function of two arguments \c *this and \a q:
   *
   * \param *this is the exposent, it must be > 1
   * \param q is the shift, it must be > 0
   *
+  * \note This function supports only float and double scalar types. To support other scalar types, the user has
+  * to provide implementations of zeta(T,T) for any scalar type T to be supported.
+  *
+  * This method is an alias for zeta(*this,q);
+  *
   * \sa Eigen::zeta()
   */
 template<typename DerivedQ>
diff --git a/Eigen/src/plugins/ArrayCwiseUnaryOps.h b/Eigen/src/plugins/ArrayCwiseUnaryOps.h
index 8b6f1d475..502e3aa1c 100644
--- a/Eigen/src/plugins/ArrayCwiseUnaryOps.h
+++ b/Eigen/src/plugins/ArrayCwiseUnaryOps.h
@@ -311,7 +311,11 @@ cosh() const
   * Example: \include Cwise_lgamma.cpp
   * Output: \verbinclude Cwise_lgamma.out
   *
-  * \sa cos(), sin(), tan()
+  * \note This function supports only float and double scalar types in c++11 mode. To support other scalar types,
+  * or float/double in non c++11 mode, the user has to provide implementations of lgamma(T) for any scalar
+  * type T to be supported.
+  *
+  * \sa digamma()
   */
 inline const LgammaReturnType
 lgamma() const
@@ -321,7 +325,11 @@ lgamma() const
 
 /** \returns an expression of the coefficient-wise digamma (psi, derivative of lgamma).
   *
-  * \sa cos(), sin(), tan()
+  * \note This function supports only float and double scalar types. To support other scalar types,
+  * the user has to provide implementations of digamma(T) for any scalar
+  * type T to be supported.
+  *
+  * \sa Eigen::digamma(), Eigen::polygamma(), lgamma()
   */
 inline const DigammaReturnType
 digamma() const
@@ -335,7 +343,11 @@ digamma() const
   * Example: \include Cwise_erf.cpp
   * Output: \verbinclude Cwise_erf.out
   *
-  * \sa cos(), sin(), tan()
+  * \note This function supports only float and double scalar types in c++11 mode. To support other scalar types,
+  * or float/double in non c++11 mode, the user has to provide implementations of erf(T) for any scalar
+  * type T to be supported.
+  *
+  * \sa erfc()
   */
 inline const ErfReturnType
 erf() const
@@ -349,7 +361,11 @@ erf() const
   * Example: \include Cwise_erfc.cpp
   * Output: \verbinclude Cwise_erfc.out
   *
-  * \sa cos(), sin(), tan()
+  * \note This function supports only float and double scalar types in c++11 mode. To support other scalar types,
+  * or float/double in non c++11 mode, the user has to provide implementations of erfc(T) for any scalar
+  * type T to be supported.
+  *
+  * \sa erf()
   */
 inline const ErfcReturnType
 erfc() const