bessel_y (MathScript RT Module Function)
Owning Class: advanced
Requires: MathScript RT Module
Syntax
yv = bessel_y(v, x)
yv = bessel_y(v, x, 1)
[yv, error] = bessel_y(v, x)
[yv, error] = bessel_y(v, x, 1)
Legacy Name: bessely
Description
Computes the Bessel function of the second kind of a given order.
Inputs
| Name | Description |
|---|---|
| v | Specifies the order of the Bessel function. v is a real, double-precision, floating-point, positive scalar, vector, or matrix. |
| x | Specifies the value for which you want to compute the Bessel function. x is a real or complex, double-precision, floating-point scalar, vector, or matrix. |
| 1 | Scales the computation. bessel_y(v, x, 1) scales bessel_y(v, x) by exp(-abs(imag(x))). |
Outputs
| Name | Description | ||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| yv | Returns the Bessel function of the second kind. yv is a real or complex, double-precision, floating-point scalar, vector, or matrix. | ||||||||||||
| error | Returns error information about the evaluation of the Bessel function. error is a matrix of integers in which each element can return the following values.
|
Details
bessel_y(v, x) solves the following equation: x2*w''+x*w'+(x2-v2)*w = 0.
The following equation is a well-known representation for bessel_y(v, x): bessel_y(v, x) = (bessel_j(v, x)*cos(v*pi)-bessel_j(-v, x))/sin(v*pi).
Examples
X = [0:0.01:2];
YV = bessel_y(2, X);
plot(X, YV)