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std::sph_neumannl

STD：：sph[医]Neumann，STD：：sph[医]肺炎，STD：：sph[医]气动

double sph_neumann ( unsigned n, double x double sph_neumann ( unsigned n, float x double sph_neumann ( unsigned n, long double x float sph_neumannf( unsigned n, float x long double sph_neumannl( unsigned n, long double x (1)(since C++17)
double sph_neumann( unsigned n, Integral x (2)(since C++17)

1%29计算第二类球面贝塞尔函数，也称为球面Neumann函数。n和x...

2%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 order of the function
x-the argument of the function

返回值

如果没有错误发生，则返回第二类球面贝塞尔函数的值%28球面Neumann函数%29n和x，那是n

n%28x%29=%28π/2x%291/2

n

N+1/2%28x%29其中N

n%28x%29是std::cyl_neumann(n,x)%29和x≥0。

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n>=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。...

例

二次

#include <cmath>
#include <iostream>
int main()
{
    // spot check for n == 1
    double x = 1.2345;
    std::cout << "n_1(" << x << ") = " << std::sph_neumann(1, x) << '\n';
 
    // exact solution for n_1
    std::cout << "-(cos x)/x^2 - (sin x)/x = "
              << -std::cos(x)/(x*x) - std::sin(x)/x << '\n';
}

二次

产出：

二次

n_1(1.2345) = -0.981201
-(cos x)/x^2 - (sin x)/x = -0.981201

二次

外部链接

第二类球贝塞尔函数。来自MathWorld的一个Wolfram Web资源。

另见

cyl_neumanncyl_neumannfcyl_neumannl (C++17)(C++17)(C++17)cylindrical Neumann functions (function)
sph_besselsph_besselfsph_bessell (C++17)(C++17)(C++17)spherical Bessel functions (of the first kind) (function)

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