### NAME

y0, y0f, y0l, y1, y1f, y1l, yn, ynf, ynl - Bessel functions of the second kind

### SYNOPSIS

#include <math.h>

double y0(double x); double y1(double x); double yn(int n, double x);

float y0f(float x); float y1f(float x); float ynf(int n, float x);

long double y0l(long double x); long double y1l(long double x); long double ynl(int n, long double x);

Feature Test Macro Requirements for glibc (see feature_test_macros(7)):

y0(), y1(), yn(): _SVID_SOURCE || _BSD_SOURCE || _XOPEN_SOURCE y0f(), y0l(), y1f(), y1l(), ynf(), ynl(): _SVID_SOURCE || _BSD_SOURCE || _XOPEN_SOURCE >= 600

### DESCRIPTION

The y0() and y1() functions return Bessel functions of x of the second kind of orders 0 and 1, respectively. The yn() function returns the Bessel function of x of the second kind of order n.

The value of x must be positive.

The y0f() etc. and y0l() etc. functions are versions that take and return float and long double values, respectively.

### RETURN VALUE

On success, these functions return the appropriate Bessel value of the second kind for x.

If x is a NaN, a NaN is returned.

If x is negative, a domain error occurs, and the functions return -HUGE_VAL, -HUGE_VALF, or -HUGE_VALL, respectively. (POSIX.1-2001 also allows a NaN return for this case.)

If x is 0.0, a pole error occurs, and the functions return -HUGE_VAL, -HUGE_VALF, or -HUGE_VALL, respectively.

If the result underflows, a range error occurs, and the functions return 0.0

If the result overflows, a range error occurs, and the functions return -HUGE_VAL, -HUGE_VALF, or -HUGE_VALL, respectively. (POSIX.1-2001 also allows a 0.0 return for this case.)

### ERRORS

See math_error(7) for information on how to determine whether an error has occurred when calling these functions.

The following errors can occur:
Domain error: x is negative
errno is set to EDOM. An invalid floating-point exception (FE_INVALID) is raised.
Pole error: x is 0.0
errno is set to ERANGE (but see BUGS). No FE_DIVBYZERO exception is returned by fetestexcept(3) for this case.
Range error: result underflow
errno is set to ERANGE. No FE_UNDERFLOW exception is returned by fetestexcept(3) for this case.
Range error: result overflow
errno is not set for this case. An overflow floating-point exception (FE_OVERFLOW) is raised.

### CONFORMING TO

The functions returning double conform to SVr4, 4.3BSD, POSIX.1-2001. The others are non-standard functions that also exist on the BSDs.

### BUGS

On a pole error, these functions set errno to EDOM, instead of ERANGE as POSIX.1-2004 requires.

In glibc version 2.3.2 and earlier, these functions do not raise an invalid floating-point exception (FE_INVALID) when a domain error occurs.