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bessel, j0, j1, jn, y0, y1, yn - Compute Bessel functions
#include <math.h>
double j0 (double x); float j0f (float x); double j1 (double x); float j1f (float x); double jn (int n, double x); float jnf (int n, float x); double y0 (double x); float y0f (float x); double y1 (double x); float y1f (float x); double yn (int n, double x); float ynf (int n, float x);
Interfaces documented on this reference page conform to industry standards as follows:
j0(): XPG4
j1(): XPG4
jn(): XPG4
y0(): XPG4
y1(): XPG4
yn(): XPG4
Refer to the standards(5) reference page for more information about industry standards and associated tags.
The j0(), j0f(), j1(), and j1f() functions return the value of the Bessel function of the first kind of orders 0 (zero) and 1, respectively.
The jn() and jnf() functions return the value of the Bessel function of the first kind of order n.
The y0(), y0f(), y1(), and y1f() functions return the value of the Bessel functions of the second kind of orders 0 (zero) and 1, respectively.
The yn() and ynf() functions return the value of the Bessel function of the second kind of order n.
The following table describes function behavior in response to exceptional arguments:
Function | Exceptional Argument | Routine Behavior |
j0(), j1(), jn() | None | N/A |
j0f(), j1f(), jnf() | None | N/A |
y0(), y1(), yn() | x < 0 | Invalid argument |
y0f(), y1f(), ynf() | x < 0 | Invalid argument |
y0(), y1(), yn() | x = 0 | Overflow |
y0f(), y1f(), ynf() | x = 0 | Overflow |
The j1() and jn() functions can result in an underflow as x gets small. The largest value of x for which this occurs is a function of n.
The y1() and yn() functions can result in an overflow as x gets small. The largest value of x for which this occurs is a function of n.
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