More Bessel functions rework

include/kyosu/functions.hpp

@@ -54,6 +54,13 @@
 #include <kyosu/functions/cyl_bessel_j1.hpp>
 #include <kyosu/functions/cyl_bessel_jn.hpp>
 #include <kyosu/functions/cyl_bessel_y0.hpp>
+#include <kyosu/functions/cyl_bessel_y1.hpp>
+#include <kyosu/functions/cyl_bessel_yn.hpp>
+#include <kyosu/functions/cyl_bessel_h1n.hpp>
+#include <kyosu/functions/cyl_bessel_h2n.hpp>
+#include <kyosu/functions/cyl_bessel_k0.hpp>
+#include <kyosu/functions/cyl_bessel_k1.hpp>
+#include <kyosu/functions/cyl_bessel_kn.hpp>
 #include <kyosu/functions/dec.hpp>
 #include <kyosu/functions/deta.hpp>
 #include <kyosu/functions/digamma.hpp>

include/kyosu/functions/cyl_bessel_h1n.hpp

@@ -0,0 +1,78 @@
+//======================================================================================================================
+/*
+  Kyosu - Complex Without Complexes
+  Copyright: KYOSU Contributors & Maintainers
+  SPDX-License-Identifier: BSL-1.0
+*/
+//======================================================================================================================
+#pragma once
+
+#include <kyosu/details/invoke.hpp>
+#include <eve/module/bessel.hpp>
+
+namespace kyosu::tags
+{
+  struct callable_cyl_bessel_h1n: eve::elementwise
+  {
+    using callable_tag_type = callable_cyl_bessel_h1n;
+
+    KYOSU_DEFERS_CALLABLE(cyl_bessel_h1n_);
+
+    template<eve::ordered_value N, eve::floating_ordered_value T>
+    static KYOSU_FORCEINLINE auto deferred_call(auto, N n, T const& z) noexcept
+    {
+      using e_t = eve::element_type_t<T>;
+      return complex(cyl_bessel_jn(n, z), cyl_bessel_yn(n, z));
+    }
+
+    template<typename N, typename T>
+    KYOSU_FORCEINLINE auto operator()(N const & target0, T const& target1) const noexcept
+    -> decltype(eve::tag_invoke(*this, target0, target1))
+    {
+      return eve::tag_invoke(*this, target0, target1);
+    }
+
+    template<typename... T>
+    eve::unsupported_call<callable_cyl_bessel_h1n(T&&...)> operator()(T&&... x) const
+    requires(!requires { eve::tag_invoke(*this, KYOSU_FWD(x)...); }) = delete;
+  };
+}
+
+namespace kyosu
+{
+//======================================================================================================================
+//! @addtogroup functions
+//! @{
+//!   @var cyl_bessel_h1n
+//!   @brief Computes the Bessel/Hankel functions of the third kind,
+//!   \f$ H_n^{(1)}(z) = J_n(z)+iY_n(z)\f$.
+//!
+//!   @code
+//!   #include <kyosu/functions.hpp>
+//!   @endcode
+//!
+//!   @groupheader{Callable Signatures}
+//!
+//!   @code
+//!   namespace kyosu
+//!   {
+//!      template<kyosu::concepts::cayley_dickson T> constexpr auto cyl_bessel_h1n(int n, T z) noexcept;
+//!      template<eve::floating_ordered_value T>     constexpr auto cyl_bessel_h1n(int n, T z) noexcept;
+//!   }
+//!   @endcode
+//!
+//!   **Parameters**
+//!
+//!     * `z`: Value to process.
+//!
+//!   **Return value**
+//!
+//!     * returns  \f$H_n^{(1)}(z)\f$.
+//!
+//!  @groupheader{Example}
+//!
+//!  @godbolt{doc/cyl_bessel_h1n.cpp}
+//! @}
+//======================================================================================================================
+inline constexpr tags::callable_cyl_bessel_h1n cyl_bessel_h1n = {};
+}

include/kyosu/functions/cyl_bessel_h2n.hpp

@@ -0,0 +1,78 @@
+//======================================================================================================================
+/*
+  Kyosu - Complex Without Complexes
+  Copyright: KYOSU Contributors & Maintainers
+  SPDX-License-Identifier: BSL-1.0
+*/
+//======================================================================================================================
+#pragma once
+
+#include <kyosu/details/invoke.hpp>
+#include <eve/module/bessel.hpp>
+
+namespace kyosu::tags
+{
+  struct callable_cyl_bessel_h2n: eve::elementwise
+  {
+    using callable_tag_type = callable_cyl_bessel_h1n;
+
+    KYOSU_DEFERS_CALLABLE(cyl_bessel_h2n_);
+
+    template<eve::ordered_value N, eve::floating_ordered_value T>
+    static KYOSU_FORCEINLINE auto deferred_call(auto, N n, T const& z) noexcept
+    {
+      using e_t = eve::element_type_t<T>;
+      return complex(cyl_bessel_jn(n, z), -cyl_bessel_yn(n, z));
+    }
+
+    template<typename N, typename T>
+    KYOSU_FORCEINLINE auto operator()(N const & target0, T const& target1) const noexcept
+    -> decltype(eve::tag_invoke(*this, target0, target1))
+    {
+      return eve::tag_invoke(*this, target0, target1);
+    }
+
+    template<typename... T>
+    eve::unsupported_call<callable_cyl_bessel_h2n(T&&...)> operator()(T&&... x) const
+    requires(!requires { eve::tag_invoke(*this, KYOSU_FWD(x)...); }) = delete;
+  };
+}
+
+namespace kyosu
+{
+//======================================================================================================================
+//! @addtogroup functions
+//! @{
+//!   @var cyl_bessel_h2n
+//!   @brief Computes the Bessel/Hankel functions of the third kind ,
+//!   \f$ H_n^{(2)} =  J_n(z)-iY_n(z)\f$.
+//!
+//!   @code
+//!   #include <kyosu/functions.hpp>
+//!   @endcode
+//!
+//!   @groupheader{Callable Signatures}
+//!
+//!   @code
+//!   namespace kyosu
+//!   {
+//!      template<kyosu::concepts::cayley_dickson T> constexpr auto cyl_bessel_h2n(int n, T z) noexcept;
+//!      template<eve::floating_ordered_value T>     constexpr auto cyl_bessel_h2n(int n, T z) noexcept;
+//!   }
+//!   @endcode
+//!
+//!   **Parameters**
+//!
+//!     * `z`: Value to process.
+//!
+//!   **Return value**
+//!
+//!     * return  \f$H_n^{(2)}(z)\f$.
+//!
+//!  @groupheader{Example}
+//!
+//!  @godbolt{doc/cyl_bessel_h2n.cpp}
+//! @}
+//======================================================================================================================
+inline constexpr tags::callable_cyl_bessel_h2n cyl_bessel_h2n = {};
+}

include/kyosu/functions/cyl_bessel_i0.hpp

@@ -39,11 +39,10 @@ namespace kyosu
 //! @addtogroup functions
 //! @{
 //!   @var cyl_bessel_i0
-//!   @brief Computes  the Bessel function of the first kind,
-//!   \f$ J_0(x)=\frac1{\pi }\int _{0}^{\pi}\cos(x\sin \tau)
-//!   \,\mathrm {d} \tau \f$ extended to the complex plane and cayley_dickson values.
+//!   @brief Computes  the modified Bessel function of the first kind \f$I_{0}(x)=J_{0}(ix)\f$
+//!   extended to the complex plane and cayley_dickson algebras.
 //!
-//!   In the real field, it is the solution of \f$ x^{2}y''+xy'+x^2y=0\f$ for which \f$ y(0) = 1\f$.
+//!   It is the solution of \f$ x^{2}y''+xy'+x^2y=0\f$ for which \f$ y(0) = 1\f$.
 //!
 //!   @code
 //!   #include <kyosu/functions.hpp>
@@ -65,7 +64,7 @@ namespace kyosu
 //!
 //!   **Return value**
 //!
-//!     * return the cylindrical \f$J_0(z)\f$.
+//!     * returns \f$I_0(z)\f$.
 //!
 //!  @groupheader{Example}
 //!

include/kyosu/functions/cyl_bessel_i1.hpp

@@ -39,11 +39,10 @@ namespace kyosu
 //! @addtogroup functions
 //! @{
 //!   @var cyl_bessel_i1
-//!   @brief Computes  the Bessel function of the first kind,
-//!   \f$ J_0(x)=\frac1{\pi }\int _{0}^{\pi}\cos(x\sin \tau)
-//!   \,\mathrm {d} \tau \f$ extended to the complex plane and cayley_dickson values.
+//!   @brief Computes  the modified Bessel function of the first kind,
+//!   \f$ I_1(x)= _iJ_1(ix) \f$ extended to the complex plane and cayley_dickson algebras.
 //!
-//!   In the real field, it is the solution of \f$ x^{2}y''+xy'+x^2y=0\f$ for which \f$ y(0) = 1\f$.
+//!   It is the solution of \f$ x^{2}y''+xy'+x^2y=0\f$ for which \f$ y(0) = 0\f$.
 //!
 //!   @code
 //!   #include <kyosu/functions.hpp>
@@ -65,7 +64,7 @@ namespace kyosu
 //!
 //!   **Return value**
 //!
-//!     * return the cylindrical \f$J_0(z)\f$.
+//!     * returns \f$I_1(z)\f$.
 //!
 //!  @groupheader{Example}
 //!

include/kyosu/functions/cyl_bessel_in.hpp

@@ -39,11 +39,11 @@ namespace kyosu
 //======================================================================================================================
 //! @addtogroup functions
 //! @{
-//!   @brief Computes the Bessel functions of the first kind,
-//!   \f$ J_{n}(x)=\sum_{p=0}^{\infty}{\frac{(-1)^p}{p!\,\Gamma (p+n +1)}}
-//!   {\left({x \over 2}\right)}^{2p+n }\f$.
+//!   @var cyl_bessel_in
+//!   @brief Computes the modified Bessel functions of the first kind \f$I_{n}(x)=i^{-n}J_{n }(ix)\f$,
+//!   extended to the complex plane and cayley_dickson algebras.
 //!
-//!   In the real field, it is the solution of \f$ x^{2}y''+xy'+(x^2-n^2)y=0\f$ for which
+//!   It is the solution of \f$ x^{2}y''+xy'+(x^2+n^2)y=0\f$ for which
 //!   \f$ y(0) = 0\f$ if \f$n \ne 0\f$ else \f$1\f$.
 //!
 //!   @code
@@ -55,8 +55,8 @@ namespace kyosu
 //!   @code
 //!   namespace kyosu
 //!   {
-//!      template<kyosu::concepts::cayley_dickson T>                                constexpr auto cyl_bessel_in(int n, T z) noexcept;
-//!      template<eve::floating_ordered_value N, eve::floating_ordered_value T>     constexpr T    cyl_bessel_in(N n, T z) noexcept;
+//!      template<kyosu::concepts::cayley_dickson T> constexpr auto cyl_bessel_in(int n, T z) noexcept;
+//!      template<eve::floating_ordered_value T>     constexpr T    cyl_bessel_in(int n, T z) noexcept;
 //!   }
 //!   @endcode
 //!
@@ -66,9 +66,7 @@ namespace kyosu
 //!
 //!   **Return value**
 //!
-//!     * return the cylindrical \f$J_n(z)\f$.
-//!
-//!  @warning Up to now the cayley_dickson versions have only been imlemented dor scalar int values of n.
+//!     * returns \f$J_n(z)\f$.
 //!
 //!  @groupheader{Example}
 //!

include/kyosu/functions/cyl_bessel_j0.hpp

@@ -41,9 +41,9 @@ namespace kyosu
 //!   @var cyl_bessel_j0
 //!   @brief Computes  the Bessel function of the first kind,
 //!   \f$ J_0(x)=\frac1{\pi }\int _{0}^{\pi}\cos(x\sin \tau)
-//!   \,\mathrm {d} \tau \f$ extended to the complex plane and cayley_dickson values.
+//!   \,\mathrm {d} \tau \f$ extended to the complex plane and cayley_dickson algebras.
 //!
-//!   In the real field, it is the solution of \f$ x^{2}y''+xy'+x^2y=0\f$ for which \f$ y(0) = 1\f$.
+//!   It is the solution of \f$ x^{2}y''+xy'+x^2y=0\f$ for which \f$ y(0) = 1\f$.
 //!
 //!   @code
 //!   #include <kyosu/functions.hpp>
@@ -65,7 +65,7 @@ namespace kyosu
 //!
 //!   **Return value**
 //!
-//!     * return the cylindrical \f$J_0(z)\f$.
+//!     * returns \f$J_0(z)\f$.
 //!
 //!  @groupheader{Example}
 //!

include/kyosu/functions/cyl_bessel_j1.hpp

@@ -42,8 +42,7 @@ namespace kyosu
 //!   @brief Computes the Bessel function of the first kind,
 //!   \f$ J_1(x)=\frac1{\pi }\int _{0}^{\pi}\cos(\tau-x\sin \tau )\,\mathrm {d} \tau \f$
 //!   extended to the complex plane and cayley_dickson values.
-//!
-//!   In the real field, it is the solution of \f$ x^{2}y''+xy'+x^2y=0\f$ for which \f$ y(0) = 1\f$.
+//!   It is the solution of \f$ x^{2}y''+xy'+x^2y=0\f$ for which \f$ y(0) = 1\f$.
 //!
 //!   @code
 //!   #include <kyosu/functions.hpp>
@@ -65,7 +64,7 @@ namespace kyosu
 //!
 //!   **Return value**
 //!
-//!     * return the cylindrical \f$J_0(z)\f$.
+//!     * returns \f$J_0(z)\f$.
 //!
 //!  @groupheader{Example}
 //!

include/kyosu/functions/cyl_bessel_jn.hpp

@@ -39,11 +39,13 @@ namespace kyosu
 //======================================================================================================================
 //! @addtogroup functions
 //! @{
+//!   @var cyl_bessel_jn
 //!   @brief Computes the Bessel functions of the first kind,
 //!   \f$ J_{n}(x)=\sum_{p=0}^{\infty}{\frac{(-1)^p}{p!\,\Gamma (p+n +1)}}
-//!   {\left({x \over 2}\right)}^{2p+n }\f$.
+//!   {\left({x \over 2}\right)}^{2p+n }\f$
+//!   extended to the complex plane and cayley_dickson values.
 //!
-//!   In the real field, it is the solution of \f$ x^{2}y''+xy'+(x^2-n^2)y=0\f$ for which
+//!   It is the solution of \f$ x^{2}y''+xy'+(x^2-n^2)y=0\f$ for which
 //!   \f$ y(0) = 0\f$ if \f$n \ne 0\f$ else \f$1\f$.
 //!
 //!   @code
@@ -55,8 +57,8 @@ namespace kyosu
 //!   @code
 //!   namespace kyosu
 //!   {
-//!      template<kyosu::concepts::cayley_dickson T>                                constexpr auto cyl_bessel_jn(int n, T z) noexcept;
-//!      template<eve::floating_ordered_value N, eve::floating_ordered_value T>     constexpr T    cyl_bessel_jn(N n, T z) noexcept;
+//!      template<kyosu::concepts::cayley_dickson T> constexpr auto cyl_bessel_jn(int n, T z) noexcept;
+//!      template<eve::floating_ordered_value T>     constexpr T    cyl_bessel_jn(int n, T z) noexcept;
 //!   }
 //!   @endcode
 //!
@@ -66,9 +68,7 @@ namespace kyosu
 //!
 //!   **Return value**
 //!
-//!     * return the cylindrical \f$J_n(z)\f$.
-//!
-//!  @warning Up to now the cayley_dickson versions have only been imlemented dor scalar int values of n.
+//!     * returns \f$J_n(z)\f$.
 //!
 //!  @groupheader{Example}
 //!