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File poly_hermite.tcc

// Special functions -*- C++ -*-

// Copyright (C) 2006-2018 Free Software Foundation, Inc.
//
// This file is part of the GNU ISO C++ Library.  This library is free
// software; you can redistribute it and/or modify it under the
// terms of the GNU General Public License as published by the
// Free Software Foundation; either version 3, or (at your option)
// any later version.
//
// This library is distributed in the hope that it will be useful,
// but WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
// GNU General Public License for more details.
//
// Under Section 7 of GPL version 3, you are granted additional
// permissions described in the GCC Runtime Library Exception, version
// 3.1, as published by the Free Software Foundation.

// You should have received a copy of the GNU General Public License and
// a copy of the GCC Runtime Library Exception along with this program;
// see the files COPYING3 and COPYING.RUNTIME respectively.  If not, see
// <http://www.gnu.org/licenses/>.

/** @file tr1/poly_hermite.tcc
 *  This is an internal header file, included by other library headers.
 *  Do not attempt to use it directly. @headername{tr1/cmath}
 */

//
// ISO C++ 14882 TR1: 5.2  Special functions
//

// Written by Edward Smith-Rowland based on:
//   (1) Handbook of Mathematical Functions,
//       Ed. Milton Abramowitz and Irene A. Stegun,
//       Dover Publications, Section 22 pp. 773-802

#ifndef _GLIBCXX_TR1_POLY_HERMITE_TCC
#define _GLIBCXX_TR1_POLY_HERMITE_TCC 1

namespace std _GLIBCXX_VISIBILITY(default)
{
_GLIBCXX_BEGIN_NAMESPACE_VERSION

#if _GLIBCXX_USE_STD_SPEC_FUNCS
#elif defined(_GLIBCXX_TR1_CMATH)
namespace tr1
{
#else
# error do not include this header directly, use <cmath> or <tr1/cmath>
#endif
  // [5.2] Special functions

// Implementation-space details.
  namespace __detail
  {
    /**
     *   @brief This routine returns the Hermite polynomial
     *          of order n: \f$ H_n(x) \f$ by recursion on n.
     * 
     *   The Hermite polynomial is defined by:
     *   @f[
     *     H_n(x) = (-1)^n e^{x^2} \frac{d^n}{dx^n} e^{-x^2}
     *   @f]
     *
     *   @param __n The order of the Hermite polynomial.
     *   @param __x The argument of the Hermite polynomial.
     *   @return The value of the Hermite polynomial of order n
     *           and argument x.
     */
    template<typename _Tp>
    _Tp
    __poly_hermite_recursion(unsigned int __n, _Tp __x)
    {
      //  Compute H_0.
      _Tp __H_0 = 1;
      if (__n == 0)
        return __H_0;

//  Compute H_1.
      _Tp __H_1 = 2 * __x;
      if (__n == 1)
        return __H_1;

//  Compute H_n.
      _Tp __H_n, __H_nm1, __H_nm2;
      unsigned int __i;
      for  (__H_nm2 = __H_0, __H_nm1 = __H_1, __i = 2; __i <= __n; ++__i)
        {
          __H_n = 2 * (__x * __H_nm1 - (__i - 1) * __H_nm2);
          __H_nm2 = __H_nm1;
          __H_nm1 = __H_n;
        }

return __H_n;
    }

/**
     *   @brief This routine returns the Hermite polynomial
     *          of order n: \f$ H_n(x) \f$.
     * 
     *   The Hermite polynomial is defined by:
     *   @f[
     *     H_n(x) = (-1)^n e^{x^2} \frac{d^n}{dx^n} e^{-x^2}
     *   @f]
     *
     *   @param __n The order of the Hermite polynomial.
     *   @param __x The argument of the Hermite polynomial.
     *   @return The value of the Hermite polynomial of order n
     *           and argument x.
     */
    template<typename _Tp>
    inline _Tp
    __poly_hermite(unsigned int __n, _Tp __x)
    {
      if (__isnan(__x))
        return std::numeric_limits<_Tp>::quiet_NaN();
      else
        return __poly_hermite_recursion(__n, __x);
    }
  } // namespace __detail
#if ! _GLIBCXX_USE_STD_SPEC_FUNCS && defined(_GLIBCXX_TR1_CMATH)
} // namespace tr1
#endif

_GLIBCXX_END_NAMESPACE_VERSION
}

#endif // _GLIBCXX_TR1_POLY_HERMITE_TCC

Name	Type	Size	Permission	Last Modified	Actions
.	DIR	-	drwxr-xr-x	2025-08-28 10:58:25
..	DIR	-	drwxr-xr-x	2025-08-28 10:58:25
array	text/x-c	6.8 KB	-rw-r--r--	2025-08-26 09:45:04
bessel_function.tcc	text/x-c	21.95 KB	-rw-r--r--	2025-08-26 09:45:04
beta_function.tcc	text/plain	5.85 KB	-rw-r--r--	2025-08-26 09:45:04
ccomplex	text/x-c	1.23 KB	-rw-r--r--	2025-08-26 09:45:04
cctype	text/x-c	1.38 KB	-rw-r--r--	2025-08-26 09:45:04
cfenv	text/x-c	1.96 KB	-rw-r--r--	2025-08-26 09:45:04
cfloat	text/x-c	1.35 KB	-rw-r--r--	2025-08-26 09:45:04
cinttypes	text/x-c	2.2 KB	-rw-r--r--	2025-08-26 09:45:04
climits	text/x-c	1.42 KB	-rw-r--r--	2025-08-26 09:45:04
cmath	text/x-c	42.78 KB	-rw-r--r--	2025-08-26 09:45:04
complex	text/x-c	12.09 KB	-rw-r--r--	2025-08-26 09:45:04
complex.h	text/x-c	1.23 KB	-rw-r--r--	2025-08-26 09:45:04
cstdarg	text/x-c	1.22 KB	-rw-r--r--	2025-08-26 09:45:04
cstdbool	text/x-c	1.31 KB	-rw-r--r--	2025-08-26 09:45:04
cstdint	text/x-c	2.56 KB	-rw-r--r--	2025-08-26 09:45:04
cstdio	text/x-c	1.45 KB	-rw-r--r--	2025-08-26 09:45:04
cstdlib	text/x-c	1.75 KB	-rw-r--r--	2025-08-26 09:45:04
ctgmath	text/x-c	1.22 KB	-rw-r--r--	2025-08-26 09:45:04
ctime	text/x-c	1.21 KB	-rw-r--r--	2025-08-26 09:45:04
ctype.h	text/x-c	1.18 KB	-rw-r--r--	2025-08-26 09:45:04
cwchar	text/x-c	1.68 KB	-rw-r--r--	2025-08-26 09:45:04
cwctype	text/x-c	1.42 KB	-rw-r--r--	2025-08-26 09:45:04
ell_integral.tcc	text/plain	27.07 KB	-rw-r--r--	2025-08-26 09:45:04
exp_integral.tcc	text/x-c	15.63 KB	-rw-r--r--	2025-08-26 09:45:04
fenv.h	text/x-c	1.18 KB	-rw-r--r--	2025-08-26 09:45:04
float.h	text/x-c	1.18 KB	-rw-r--r--	2025-08-26 09:45:04
functional	text/x-c	68.89 KB	-rw-r--r--	2025-08-26 09:45:04
functional_hash.h	text/plain	5.9 KB	-rw-r--r--	2025-08-26 09:45:04
gamma.tcc	text/x-c	14.34 KB	-rw-r--r--	2025-08-26 09:45:04
hashtable.h	text/x-c	40.56 KB	-rw-r--r--	2025-08-26 09:45:04
hashtable_policy.h	text/plain	24.5 KB	-rw-r--r--	2025-08-26 09:45:04
hypergeometric.tcc	text/plain	27.41 KB	-rw-r--r--	2025-08-26 09:45:04
inttypes.h	text/x-c	1.24 KB	-rw-r--r--	2025-08-26 09:45:04
legendre_function.tcc	text/x-c	10.65 KB	-rw-r--r--	2025-08-26 09:45:04
limits.h	text/x-c	1.19 KB	-rw-r--r--	2025-08-26 09:45:04
math.h	text/x-c	4.45 KB	-rw-r--r--	2025-08-26 09:45:04
memory	text/x-c	1.75 KB	-rw-r--r--	2025-08-26 09:45:04
modified_bessel_func.tcc	text/x-c	15.94 KB	-rw-r--r--	2025-08-26 09:45:04
poly_hermite.tcc	text/plain	3.83 KB	-rw-r--r--	2025-08-26 09:45:04
poly_laguerre.tcc	text/plain	11.4 KB	-rw-r--r--	2025-08-26 09:45:04
random	text/x-c	1.55 KB	-rw-r--r--	2025-08-26 09:45:04
random.h	text/plain	71.41 KB	-rw-r--r--	2025-08-26 09:45:04
random.tcc	text/plain	52.66 KB	-rw-r--r--	2025-08-26 09:45:04
regex	text/x-c	90.7 KB	-rw-r--r--	2025-08-26 09:45:04
riemann_zeta.tcc	text/x-c	13.73 KB	-rw-r--r--	2025-08-26 09:45:04
shared_ptr.h	text/plain	31.84 KB	-rw-r--r--	2025-08-26 09:45:04
special_function_util.h	text/plain	4.94 KB	-rw-r--r--	2025-08-26 09:45:04
stdarg.h	text/x-c	1.19 KB	-rw-r--r--	2025-08-26 09:45:04
stdbool.h	text/x-c	1.19 KB	-rw-r--r--	2025-08-26 09:45:04
stdint.h	text/x-c	1.19 KB	-rw-r--r--	2025-08-26 09:45:04
stdio.h	text/x-c	1.18 KB	-rw-r--r--	2025-08-26 09:45:04
stdlib.h	text/x-c	1.45 KB	-rw-r--r--	2025-08-26 09:45:04
tgmath.h	text/x-c	1.23 KB	-rw-r--r--	2025-08-26 09:45:04
tuple	text/x-c	11.83 KB	-rw-r--r--	2025-08-26 09:45:04
type_traits	text/x-c	18.57 KB	-rw-r--r--	2025-08-26 09:45:04
unordered_map	text/x-c	1.54 KB	-rw-r--r--	2025-08-26 09:45:04
unordered_map.h	text/plain	9.98 KB	-rw-r--r--	2025-08-26 09:45:04
unordered_set	text/x-c	1.54 KB	-rw-r--r--	2025-08-26 09:45:04
unordered_set.h	text/plain	9.32 KB	-rw-r--r--	2025-08-26 09:45:04
utility	text/x-c	3.15 KB	-rw-r--r--	2025-08-26 09:45:04
wchar.h	text/x-c	1.22 KB	-rw-r--r--	2025-08-26 09:45:04
wctype.h	text/x-c	1.23 KB	-rw-r--r--	2025-08-26 09:45:04

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