Y1 — Y | CodeCogs

Bessel function of second kind with order one.

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Interface

#include <codecogs/maths/special/bessel/y/y1.h>

using namespace Maths::Special::Bessel::Y;

double Y1(double x)

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

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

(1)

with $I_1(x)$ and $I_{-1}(x)$ being the other solutions. See 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

Parameters

input

Interactive Calculator

Result –