std::sph_be...:sph_bessell(3)

🌸 NAME 🌸

okay so this is the C++ Standard Libary manual, page std::sph_be...:sph_bessell(3) — and the NAME section is literally std::sph_bessel,std::sph_besself,std::sph_bessell - std::sph_bessel,std::sph_besself,std::sph_bessell. The trio is std::sph_bessel, std::sph_besself, and std::sph_bessell, and yes bestie, that dash-and-repeat is giving very “the name is the name” energy. 💅

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✨ Synopsis ✨

Defined in header <cmath>.

float       sph_bessel ( unsigned int n, float x );        (since C++17)
double      sph_bessel ( unsigned int n, double x );       (until C++23)
long double sph_bessel ( unsigned int n, long double x );
/* floating-point-type */ sph_bessel( unsigned int n,
                                      /* floating-point-type */ x );
(1) (since C++23)

float       sph_besself( unsigned int n, float x );
(2) (since C++17)

long double sph_bessell( unsigned int n, long double x );
(3) (since C++17)

1-3) Computes the spherical Bessel function of the first kind of n and x.

The library provides overloads of std::sph_bessel for all cv-unqualified floating-point types as the type of the parameter x. (since C++23)

Additional overloads also say: Defined in header <cmath>.

template< class Integer >
double      sph_bessel ( unsigned int n, Integer x );
(A) (since C++17)

A) Additional overloads are provided for all integer types, which are treated as double.

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🎀 Parameters 🎀

• n — the order of the function
• x — the argument of the function

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🦋 Return value 🦋

If no errors occur, returns the value of the spherical Bessel function of the first kind of n and x, that is j_n(x) = (π/2x)1/2 J_{n+1/2}(x) where J_n(x) is std::cyl_bessel_j(n, x) and x≥0.

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🌸 Error handling 🌸

Errors may be reported as specified in math_errhandling.

• If the argument is NaN, NaN is returned and domain error is not reported.
• If n≥128, the behavior is implementation-defined.

🚨 bestie, that n≥128 line is not a vibe-check suggestion — it’s literally implementation-defined behavior.

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💜 Notes 💜

• Implementations that do not support C++17, but support ISO 29124:2010, provide this function if __STDCPP_MATH_SPEC_FUNCS__ is defined by the implementation to a value at least 201003L and if the user defines __STDCPP_WANT_MATH_SPEC_FUNCS__ before including any standard library headers.
• Implementations that do not support ISO 29124:2010 but support TR 19768:2007 (TR1), provide this function in the header tr1/cmath and namespace std::tr1.
• An implementation of this function is also available in boost.math.
• The additional overloads are not required to be provided exactly as (A). They only need to be sufficient to ensure that for their argument num of integer type, std::sph_bessel(int_num, num) has the same effect as std::sph_bessel(int_num, static_cast<double>(num)).

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🍓 Example 🍓

The page says // Run this code — so here’s the code, bestie:

#include <cmath>
#include <iostream>

int main()
{
    // spot check for n == 1
    double x = 1.2345;
    std::cout << "j_1(" << x << ") = " << std::sph_bessel(1, x) << '\n';

    // exact solution for j_1
    std::cout << "sin(x)/x² - cos(x)/x = "
              << std::sin(x) / (x * x) - std::cos(x) / x << '\n';
}

💖 Output 💖

j_1(1.2345) = 0.352106
sin(x)/x² - cos(x)/x = 0.352106

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🌈 See also 🌈

• cyl_bessel_j — cylindrical Bessel functions (of the first kind), (C++17), (function)
• cyl_bessel_jf — cylindrical Bessel functions (of the first kind), (C++17), (function)
• cyl_bessel_jl — cylindrical Bessel functions (of the first kind), (C++17), (function)
• sph_neumann — spherical Neumann functions, (C++17), (function)
• sph_neumannf — spherical Neumann functions, (C++17), (function)
• sph_neumannl — spherical Neumann functions, (C++17), (function)

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⭐ External links ⭐

Weisstein, Eric W. "Spherical Bessel Function of the First Kind." From MathWorld — A Wolfram Web Resource.

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and that’s the whole page, bestie 🫶✨ — source/version: http://cppreference.com, date: 2024.06.10, footer title: std::sph_be...:sph_bessell(3).