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std::laguerrel

STD：Laguerre，STD：：laguerref，std：：laguerrel

double laguerre( unsigned int n, double x double laguerre( unsigned int n, float x double laguerre( unsigned int n, long double x float laguerref( unsigned int n, float x long double laguerrel( unsigned int n, long double x (1)(since C++17)
double laguerre( unsigned int n, Integral x (2)(since C++17)

1%29计算非关联的Laguerre多项式程度n和争论x

4%29一组过载或接受任意参数的函数模板积分型将参数转换为double...

参数

n-the degree of the polymonial, a value of unsigned integer type
x-the argument, a value of a floating-point or integral type

返回值

如果没有错误发生，则非相关的Laguerre多项式的值x，那就是

前

*。

n%21

DN

*。

dxn

%28 xn

e-x%29，返回。

错误处理

错误可以按数学[医]错误处理...

  • 如果参数为nan，则返回nan，并且不报告域错误。

  • 如果x为负值，则可能发生域错误。

  • 如果n大于或等于128，则行为是实现定义的。

注记

不支持C++17但支持的实现ISO 29124：2010，则提供此功能__STDCPP_MATH_SPEC_FUNCS__由实现定义为值至少为201003L，且用户定义__STDCPP_WANT_MATH_SPEC_FUNCS__在包含任何标准库头之前。

不支持iso 29124：2010但支持tr 19768：2007%28TR1%29的实现，在标头中提供此功能。tr1/cmath和命名空间std::tr1...

此功能的实现也是可以在中学里找到。...

Laguerre多项式是方程XY的多项式解，

+%281-x%29 y，

+NY=0。

前几个例子是：

  • 拉盖尔%280，x%29=1

  • Laguerre%281，x%29=-x+1

  • 拉盖尔%282，x%29=1 2。[X2

-4x+2]

  • 拉盖尔%283，x%29=1 6。[-x3

-9x2

-18x+6]

例

二次

#define __STDCPP_WANT_MATH_SPEC_FUNCS__ 1
#include <cmath>
#include <iostream>
double L1(double x) { return -x + 1; }
double L2(double x) { return 0.5*(x*x-4*x+2 }
int main()
{
    // spot-checks
    std::cout << std::laguerre(1, 0.5) << '=' << L1(0.5) << '\n'
              << std::laguerre(2, 0.5) << '=' << L2(0.5) << '\n';
}

二次

产出：

二次

0.5=0.5
0.125=0.125

二次

另见

assoc_laguerreassoc_laguerrefassoc_laguerrel (C++17)(C++17)(C++17)associated Laguerre polynomials (function)

外部链接

Weisstein，Eric W.“Laguerre多项式”来自MathWorld的一个Wolfram Web资源。

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