Y1

Bessel function of second kind with order one.

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Y1
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Y1

doubleY1( double x )

A Bessel function of the second kind with order one $\inline Y_1(x)$ is a solution to differential equation

$x^2 \frac{d^2y}{dx^2} + x \frac{dy}{dx} + (x^2 - 1)y = 0$

(2)

with $\inline I_1(x)$ and $\inline I_{-1}(x)$ being the other solutions. 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/y1.h>
int main()
{
  for(double x=1; x<7; x+=1)
  {
    double y=Maths::Special::Bessel::Y::Y1(x);
    printf("\n Y1(%.1lf)=%lf", x,y);
  }
  return 0;
}

Output:

Y1(1.0)=-0.781213
Y1(2.0)=-0.107032
Y1(3.0)=0.324674
Y1(4.0)=0.397926
Y1(5.0)=0.147863
Y1(6.0)=-0.175010

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