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array	6.82 KB	-rw-r--r--
bessel_function.tcc	22.4 KB	-rw-r--r--
beta_function.tcc	5.85 KB	-rw-r--r--
ccomplex	1.23 KB	-rw-r--r--
cctype	1.38 KB	-rw-r--r--
cfenv	1.96 KB	-rw-r--r--
cfloat	1.35 KB	-rw-r--r--
cinttypes	2.2 KB	-rw-r--r--
climits	1.42 KB	-rw-r--r--
cmath	42.78 KB	-rw-r--r--
complex	12.09 KB	-rw-r--r--
complex.h	1.23 KB	-rw-r--r--
cstdarg	1.22 KB	-rw-r--r--
cstdbool	1.31 KB	-rw-r--r--
cstdint	2.56 KB	-rw-r--r--
cstdio	1.45 KB	-rw-r--r--
cstdlib	1.75 KB	-rw-r--r--
ctgmath	1.22 KB	-rw-r--r--
ctime	1.21 KB	-rw-r--r--
ctype.h	1.18 KB	-rw-r--r--
cwchar	1.68 KB	-rw-r--r--
cwctype	1.42 KB	-rw-r--r--
ell_integral.tcc	27.07 KB	-rw-r--r--
exp_integral.tcc	15.64 KB	-rw-r--r--
fenv.h	1.18 KB	-rw-r--r--
float.h	1.18 KB	-rw-r--r--
functional	68.89 KB	-rw-r--r--
functional_hash.h	5.9 KB	-rw-r--r--
gamma.tcc	14.34 KB	-rw-r--r--
hashtable.h	40.58 KB	-rw-r--r--
hashtable_policy.h	24.5 KB	-rw-r--r--
hypergeometric.tcc	27.41 KB	-rw-r--r--
inttypes.h	1.24 KB	-rw-r--r--
legendre_function.tcc	10.4 KB	-rw-r--r--
limits.h	1.19 KB	-rw-r--r--
math.h	4.45 KB	-rw-r--r--
memory	1.75 KB	-rw-r--r--
modified_bessel_func.tcc	15.94 KB	-rw-r--r--
poly_hermite.tcc	3.83 KB	-rw-r--r--
poly_laguerre.tcc	11.4 KB	-rw-r--r--
random	1.55 KB	-rw-r--r--
random.h	71.38 KB	-rw-r--r--
random.tcc	52.66 KB	-rw-r--r--
regex	90.74 KB	-rw-r--r--
riemann_zeta.tcc	13.74 KB	-rw-r--r--
shared_ptr.h	31.84 KB	-rw-r--r--
special_function_util.h	4.94 KB	-rw-r--r--
stdarg.h	1.19 KB	-rw-r--r--
stdbool.h	1.19 KB	-rw-r--r--
stdint.h	1.19 KB	-rw-r--r--
stdio.h	1.18 KB	-rw-r--r--
stdlib.h	1.45 KB	-rw-r--r--
tgmath.h	1.23 KB	-rw-r--r--
tuple	11.83 KB	-rw-r--r--
type_traits	18.57 KB	-rw-r--r--
unordered_map	1.54 KB	-rw-r--r--
unordered_map.h	9.98 KB	-rw-r--r--
unordered_set	1.54 KB	-rw-r--r--
unordered_set.h	9.32 KB	-rw-r--r--
utility	3.15 KB	-rw-r--r--
wchar.h	1.22 KB	-rw-r--r--
wctype.h	1.23 KB	-rw-r--r--

Code Editor : poly_hermite.tcc

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

// Copyright (C) 2006-2019 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

${this.title}

Code Editor : poly_hermite.tcc