y0(3) Library Functions Manual y0(3)

# NAME¶

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

# LIBRARY¶

Math library (libm, -lm)

# 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():

```
_XOPEN_SOURCE

|| /* Since glibc 2.19: */ _DEFAULT_SOURCE

|| /* glibc <= 2.19: */ _SVID_SOURCE || _BSD_SOURCE```

y0f(), y0l(), y1f(), y1l(), ynf(), ynl():

```
_XOPEN_SOURCE >= 600

|| (_ISOC99_SOURCE && _XOPEN_SOURCE)

|| /* Since glibc 2.19: */ _DEFAULT_SOURCE

|| /* glibc <= 2.19: */ _SVID_SOURCE || _BSD_SOURCE```

# 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(), y1f(), and ynf() functions are versions that take and return float values. The y0l(), y1l(), and ynl() functions are versions that take and return long double values.

# 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:

errno is set to EDOM. An invalid floating-point exception (FE_INVALID) is raised.
errno is set to ERANGE and an FE_DIVBYZERO exception is raised (but see BUGS).
errno is set to ERANGE. No FE_UNDERFLOW exception is returned by fetestexcept(3) for this case.
errno is set to ERANGE (but see BUGS). An overflow floating-point exception (FE_OVERFLOW) is raised.

# ATTRIBUTES¶

For an explanation of the terms used in this section, see attributes(7).

 Interface Attribute Value y0 (), y0f (), y0l () Thread safety MT-Safe y1 (), y1f (), y1l () Thread safety MT-Safe yn (), ynf (), ynl () Thread safety MT-Safe

# STANDARDS¶

The functions returning double conform to SVr4, 4.3BSD, POSIX.1-2001, POSIX.1-2008. The others are nonstandard functions that also exist on the BSDs.

# BUGS¶

Before glibc 2.19, these functions misdiagnosed pole errors: errno was set to EDOM, instead of ERANGE and no FE_DIVBYZERO exception was raised.

Before glibc 2.17, did not set errno for "range error: result underflow".

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