Y0

Bessel function of second kind with zero order.

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Y0
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C++

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Y0

doubleY0( double x )

A Bessel function of the second kind with zero order $\inline Y_0(x)$ is sometimes also denoted using $\inline N_n(x)$ and is a solution to differential equation

$x^2 \frac{d^2y}{dx^2} + x \frac{dy}{dx} + (x^2)y = 0$

(2)

with $\inline I_0(x)$ being the other solution. See Maths/Special/Bessel/I/I

This solution has a regular singularity at 0.

References:

Cephes Math Library Release 2.8: June, 2000

Example 1

#include <stdio.h>
#include <codecogs/maths/special/bessel/y/y0.h>
int main()
{
  for(double x=1; x<7; x+=1)
  {
    double y=Maths::Special::Bessel::Y::Y0(x);
    printf("\n Y0(%.1lf)=%lf", x,y);
  }
  return 0;
}

Output:

Y0(1.0)=0.088257
Y0(2.0)=0.510376
Y0(3.0)=0.376850
Y0(4.0)=-0.016941
Y0(5.0)=-0.308518
Y0(6.0)=-0.288195

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