cyl_bessel_i0

auto eve::cyl_bessel_i0 = functor<cyl_bessel_i0_t>

inlineconstexpr

It is the solution of \( x^{2}y''+xy'-x^2y=0\) for which \( y(0) = 0\).

Header file

#include <eve/module/bessel.hpp>

Callable Signatures

namespace eve
{
   // Regular overload
   constexpr auto cyl_bessel_i0(floating_value auto x) -> decltype(x)           noexcept; // 1
 
   // Lanes masking
   constexpr auto cyl_bessel_i0[conditional_expr auto c](floating_value auto x) noexcept; // 2
   constexpr auto cyl_bessel_i0[logical_value auto m](floating_value auto x)    noexcept; // 2
}

Parameters

• x: positive floating argument.
• c: Conditional expression masking the operation.
• m: Logical value masking the operation.

Return value

1. The value of \( \displaystyle I_0(x)=\frac1{\pi}\int_{0}^{\pi}e^{x\cos\tau} \,\mathrm{d}\tau\) is returned.
2. The operation is performed conditionnaly.

External references

• C++ standard reference: cyl_bessel_i
• Wikipedia: Bessel Functions
• DLMF: Modified Bessel Functions

Example

// revision 1
#include <eve/module/bessel.hpp>
#include <iostream>
 
eve::wide<double> wf0([](auto i, auto c)->double{ return 2*(i+c/2);});
eve::wide         wf1{0.5, -1.5, 0.1, -1.0, 19.0, 25.0, 21.5, 10000.0};
 
int main()
{
   std::cout << "<- wf0 = " << wf0 << "\n";
   std::cout << "<- wf1 = " << wf1 << "\n";
 
   std::cout << "-> cyl_bessel_i0(wf0)                = " << eve::cyl_bessel_i0(wf0) << "\n";
   std::cout << "-> cyl_bessel_i0[ignore_last(2)](wf0)= " << eve::cyl_bessel_i0[eve::ignore_last(2)](wf0) << "\n";
   std::cout << "-> cyl_bessel_i0[wf0!= -2.0f](wf0)   = " << eve::cyl_bessel_i0[wf0!= -2.0f](wf0) << "\n";
   std::cout << "-> cyl_bessel_i0(wf1)                = " << eve::cyl_bessel_i0(wf1) << "\n";
}