diff --git a/include/kyosu/complex/erf.hpp b/include/kyosu/complex/erf.hpp
index cd1e58d0..fd88ff58 100644
--- a/include/kyosu/complex/erf.hpp
+++ b/include/kyosu/complex/erf.hpp
@@ -68,7 +68,7 @@ namespace kyosu
 //!
 //! **Return value**
 //!
-//!   1. a real input z is treated as if complex(z) was entered.
+//!   1. a real input z returns eve::erf(z).
 //!
 //!   2.  The value of the error function in the complex plane is returned
 //!
diff --git a/include/kyosu/complex/erfcx.hpp b/include/kyosu/complex/erfcx.hpp
index db5a0e4a..abdd8f01 100644
--- a/include/kyosu/complex/erfcx.hpp
+++ b/include/kyosu/complex/erfcx.hpp
@@ -67,7 +67,7 @@ namespace kyosu
 //!
 //! **Return value**
 //!
-//!   1. a real input z is treated as if complex(z) was entered.
+//!   1. a real input z return eve::erfcx(z).
 //!
 //!   2. The value of the normalized complementary error function is returned.
 //!
diff --git a/include/kyosu/complex/erfi.hpp b/include/kyosu/complex/erfi.hpp
index 7b69a037..5390a945 100644
--- a/include/kyosu/complex/erfi.hpp
+++ b/include/kyosu/complex/erfi.hpp
@@ -65,7 +65,7 @@ namespace kyosu
 //!
 //!   **Parameters**
 //!
-//!     * `z` : Vcomplex or real value to process.
+//!     * `z` : complex or real value to process.
 //!
 //! **Return value**
 //!
diff --git a/include/kyosu/complex/eta.hpp b/include/kyosu/complex/eta.hpp
index 0f64ba4d..1ddff424 100644
--- a/include/kyosu/complex/eta.hpp
+++ b/include/kyosu/complex/eta.hpp
@@ -64,11 +64,11 @@ namespace kyosu
 //!
 //!   **Parameters**
 //!
-//!     * `z` : Vcomplex or real value to process.
+//!     * `z` : complex or real value to process.
 //!
 //! **Return value**
 //!
-//!   Returns the Dirichlet alternating zeta function: sum \f$  \displaystyle \sum_0^\infty \frac{(-1)^n}{(n+1)^z}\f$
+//!   Returns the Dirichlet alternating zeta function: \f$  \displaystyle \sum_0^\infty \frac{(-1)^n}{(n+1)^z}\f$
 //!
 //!  @groupheader{Example}
 //!
diff --git a/include/kyosu/complex/lambda.hpp b/include/kyosu/complex/lambda.hpp
index b0aa70c4..ce0dd606 100644
--- a/include/kyosu/complex/lambda.hpp
+++ b/include/kyosu/complex/lambda.hpp
@@ -67,7 +67,7 @@ namespace kyosu
 //!
 //!   **Parameters**
 //!
-//!     * `z` : Vcomplex or real value to process.
+//!     * `z` : complex or real value to process.
 //!
 //! **Return value**
 //!
diff --git a/include/kyosu/complex/zeta.hpp b/include/kyosu/complex/zeta.hpp
index ea909afc..2f69b61a 100644
--- a/include/kyosu/complex/zeta.hpp
+++ b/include/kyosu/complex/zeta.hpp
@@ -64,7 +64,7 @@ namespace kyosu
 //!   **Parameters**
 //!
 //!     * `k` : scalar unsigned value,  parameter of the sum.
-//!     * `z` : Vcomplex or real value to process.
+//!     * `z` : complex or real value to process.
 //!
 //! **Return value**
 //!
diff --git a/include/kyosu/functions/exp.hpp b/include/kyosu/functions/exp.hpp
index 43c1cd75..3fcb71f1 100644
--- a/include/kyosu/functions/exp.hpp
+++ b/include/kyosu/functions/exp.hpp
@@ -53,7 +53,7 @@ namespace kyosu
 //!   namespace kyosu
 //!   {
 //!      template<kyosu::concepts::cayley_dickson T> constexpr T exp(T z) noexcept;
-//!      template<eve::floating_ordered_value T>              constexpr T exp(T z) noexcept;
+//!      template<eve::floating_ordered_value T>     constexpr T exp(T z) noexcept;
 //!   }
 //!   @endcode
 //!
diff --git a/include/kyosu/functions/exp10.hpp b/include/kyosu/functions/exp10.hpp
index 7d5a4f75..e209ccb0 100644
--- a/include/kyosu/functions/exp10.hpp
+++ b/include/kyosu/functions/exp10.hpp
@@ -52,8 +52,8 @@ namespace kyosu
 //!   @code
 //!   namespace kyosu
 //!   {
-//!      template<kyosu::concepts::cayley_dickson T> constexp10r T exp10(T z) noexcept;
-//!      template<eve::floating_ordered_value T>              constexp10r T exp10(T z) noexcept;
+//!      template<kyosu::concepts::cayley_dickson T> constexpr T exp10(T z) noexcept;
+//!      template<eve::floating_ordered_value T>     constexpr T exp10(T z) noexcept;
 //!   }
 //!   @endcode
 //!
diff --git a/include/kyosu/functions/exp2.hpp b/include/kyosu/functions/exp2.hpp
index 6b7a271e..236c45fd 100644
--- a/include/kyosu/functions/exp2.hpp
+++ b/include/kyosu/functions/exp2.hpp
@@ -52,8 +52,8 @@ namespace kyosu
 //!   @code
 //!   namespace kyosu
 //!   {
-//!      template<kyosu::concepts::cayley_dickson T> constexp2r T exp2(T z) noexcept;
-//!      template<eve::floating_ordered_value T>              constexp2r T exp2(T z) noexcept;
+//!      template<kyosu::concepts::cayley_dickson T> constexpr T exp2(T z) noexcept;
+//!      template<eve::floating_ordered_value T>     constexpr T exp2(T z) noexcept;
 //!   }
 //!   @endcode
 //!
diff --git a/include/kyosu/functions/exp_i.hpp b/include/kyosu/functions/exp_i.hpp
index 463f03bf..9050d649 100644
--- a/include/kyosu/functions/exp_i.hpp
+++ b/include/kyosu/functions/exp_i.hpp
@@ -44,7 +44,7 @@ namespace kyosu
 //! @addtogroup functions
 //! @{
 //!   @var exp_i
-//!   @brief Computes the exponential of the argument times i.
+//!   @brief Computes the exponential of i times the argument
 //!
 //!   **Defined in Header**
 //!
@@ -58,7 +58,7 @@ namespace kyosu
 //!   namespace kyosu
 //!   {
 //!      template<kyosu::concepts::cayley_dickson T> constexp_ir T exp_i(T z) noexcept;
-//!      template<eve::floating_ordered_value T>              constexp_ir T exp_i(T z) noexcept;
+//!      template<eve::floating_ordered_value T>     constexp_ir T exp_i(T z) noexcept;
 //!   }
 //!   @endcode
 //!
@@ -68,7 +68,7 @@ namespace kyosu
 //!
 //!   **Return value**
 //!
-//!     Returns the `exp(i*z)`.
+//!     Returns `exp(i*z)`.
 //!
 //!  @groupheader{Example}
 //!
diff --git a/include/kyosu/functions/exp_ipi.hpp b/include/kyosu/functions/exp_ipi.hpp
index 431b67e6..7814ceb2 100644
--- a/include/kyosu/functions/exp_ipi.hpp
+++ b/include/kyosu/functions/exp_ipi.hpp
@@ -44,7 +44,7 @@ namespace kyosu
 //! @addtogroup functions
 //! @{
 //!   @var exp_ipi
-//!   @brief Computes the exponential of the argument times i.
+//!   @brief Computes the exponential of \f$i\pi\f$ times the argument.
 //!
 //!   **Defined in Header**
 //!
@@ -58,7 +58,7 @@ namespace kyosu
 //!   namespace kyosu
 //!   {
 //!      template<kyosu::concepts::cayley_dickson T> constexp_ipir T exp_ipi(T z) noexcept;
-//!      template<eve::floating_ordered_value T>              constexp_ipir T exp_ipi(T z) noexcept;
+//!      template<eve::floating_ordered_value T>     constexp_ipir T exp_ipi(T z) noexcept;
 //!   }
 //!   @endcode
 //!
@@ -68,7 +68,7 @@ namespace kyosu
 //!
 //!   **Return value**
 //!
-//!     Returns the `exp(i*z)`.
+//!     Returns  `exp(i*pi(as(z))*z)`.
 //!
 //!  @groupheader{Example}
 //!
diff --git a/include/kyosu/functions/expm1.hpp b/include/kyosu/functions/expm1.hpp
index 3a3b6608..79f6d3c9 100644
--- a/include/kyosu/functions/expm1.hpp
+++ b/include/kyosu/functions/expm1.hpp
@@ -39,7 +39,7 @@ namespace kyosu
 //! @addtogroup functions
 //! @{
 //!   @var expm1
-//!   @brief Computes the expm1onential of the argument minus 1.
+//!   @brief Computes the exponential of the argument minus 1.
 //!
 //!   **Defined in Header**
 //!
@@ -53,7 +53,7 @@ namespace kyosu
 //!   namespace kyosu
 //!   {
 //!      template<kyosu::concepts::cayley_dickson T> constexpm1r T expm1(T z) noexcept;
-//!      template<eve::floating_ordered_value T>              constexpm1r T expm1(T z) noexcept;
+//!      template<eve::floating_ordered_value T>     constexpm1r T expm1(T z) noexcept;
 //!   }
 //!   @endcode
 //!
@@ -63,7 +63,7 @@ namespace kyosu
 //!
 //!   **Return value**
 //!
-//!     Returns the expm1onential of the argument minus &.
+//!     Returns the expm1onential of the argument minus 1.
 //!     for real and complex typed inputs, provisions are made to ensure good precision near zero.
 //!
 //!  @groupheader{Example}
diff --git a/include/kyosu/functions/expmx2.hpp b/include/kyosu/functions/expmx2.hpp
index 7e82b2e6..5234853d 100644
--- a/include/kyosu/functions/expmx2.hpp
+++ b/include/kyosu/functions/expmx2.hpp
@@ -52,8 +52,8 @@ namespace kyosu
 //!   @code
 //!   namespace kyosu
 //!   {
-//!      template<kyosu::concepts::cayley_dickson T> constexpmx2r T expmx2(T z) noexcept;
-//!      template<eve::floating_ordered_value T>              constexpmx2r T expmx2(T z) noexcept;
+//!      template<kyosu::concepts::cayley_dickson T> constexpr T expmx2(T z) noexcept;
+//!      template<eve::floating_ordered_value T>     constexpr T expmx2(T z) noexcept;
 //!   }
 //!   @endcode
 //!
diff --git a/include/kyosu/functions/expx2.hpp b/include/kyosu/functions/expx2.hpp
index 84d5dd30..8de316c5 100644
--- a/include/kyosu/functions/expx2.hpp
+++ b/include/kyosu/functions/expx2.hpp
@@ -52,8 +52,8 @@ namespace kyosu
 //!   @code
 //!   namespace kyosu
 //!   {
-//!      template<kyosu::concepts::cayley_dickson T> constexpx2r T expx2(T z) noexcept;
-//!      template<eve::floating_ordered_value T>              constexpx2r T expx2(T z) noexcept;
+//!      template<kyosu::concepts::cayley_dickson T> constexpr T expx2(T z) noexcept;
+//!      template<eve::floating_ordered_value T>     constexpr T expx2(T z) noexcept;
 //!   }
 //!   @endcode
 //!