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


#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);
[Note] Note
Feature Test Macro Requirements for glibc (see feature_test_macros(7)):
y0(), y1(), yn():
y0f(), y0l(), y1f(), y1l(), ynf(), ynl():
[Note] Note

Link with −lm.


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.


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.)


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.


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


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.




This page is part of release 3.52 of the Linux man-pages project. A description of the project, and information about reporting bugs, can be found at−pages/.

  Copyright 1993 David Metcalfe (
and Copyright 2008, Linux Foundation, written by Michael Kerrisk

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References consulted:
    Linux libc source code
    Lewine's _POSIX Programmer's Guide_ (O'Reilly & Associates, 1991)
    386BSD man pages
Modified Sat Jul 24 19:08:17 1993 by Rik Faith (
Modified 2002-08-25, aeb
Modified 2004-11-12 as per suggestion by Fabian Kreutz/AEB
2008-07-24, mtk, created this page, based on material from j0.3.