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**NAME**

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

**SYNOPSIS**

#include<math.h>doubley0(doublex);doubley1(doublex);doubleyn(intn,doublex);floaty0f(floatx);floaty1f(floatx);floatynf(intn,floatx);longdoubley0l(longdoublex);longdoubley1l(longdoublex);longdoubleynl(intn,longdoublex);Link with-lm. Feature Test Macro Requirements for glibc (seefeature_test_macros(7)):y0(),y1(),yn(): _SVID_SOURCE || _BSD_SOURCE || _XOPEN_SOURCEy0f(),y0l(),y1f(),y1l(),ynf(),ynl(): _SVID_SOURCE || _BSD_SOURCE || _XOPEN_SOURCE >= 600

**DESCRIPTION**

They0() andy1() functions return Bessel functions ofxof the second kind of orders 0 and 1, respectively. Theyn() function returns the Bessel function ofxof the second kind of ordern. The value ofxmust be positive. They0f() etc. andy0l() etc. functions are versions that take and returnfloatandlongdoublevalues, respectively.

**RETURN** **VALUE**

On success, these functions return the appropriate Bessel value of the second kind forx. Ifxis a NaN, a NaN is returned. Ifxis 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.) Ifxis 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**

Seemath_error(7) for information on how to determine whether an error has occurred when calling these functions. The following errors can occur: Domain error:xis negativeerrnois set toEDOM. An invalid floating-point exception (FE_INVALID) is raised. Pole error:xis 0.0errnois set toERANGE(but see BUGS). NoFE_DIVBYZEROexception is returned byfetestexcept(3) for this case. Range error: result underflowerrnois set toERANGE. NoFE_UNDERFLOWexception is returned byfetestexcept(3) for this case. Range error: result overflowerrnois not set for this case. An overflow floating-point exception (FE_OVERFLOW) is raised.

**CONFORMING** **TO**

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

**BUGS**

On a pole error, these functions seterrnotoEDOM, instead ofERANGEas 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.

**SEE** **ALSO**

j0(3)

**COLOPHON**

This page is part of release 3.35 of the Linuxman-pagesproject. A description of the project, and information about reporting bugs, can be found at http://man7.org/linux/man- pages/. 2008-08-10 Y0(3)