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

       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 │
       └─────────────────────────────────────────────────────────────────────────────┴───────────────┴─────────┘

       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.

       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 longdouble values.

       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 and an FE_DIVBYZERO exception is raised (but see BUGS).

       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  set  to  ERANGE  (but see BUGS).  An overflow floating-point exception (FE_OVERFLOW) is
              raised.

y0()
       y1()
       yn()   SVr4, 4.3BSD, POSIX.1-2001.

       Others:
              BSD.

       Math library (libm, -lm)

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

       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.)

j0(3)

Linux man-pages 6.9.1                              2024-05-02                                              y0(3)

y0()
       y1()
       yn()   POSIX.1-2008.

       Others:
              BSD.

#include<math.h>doubley0(doublex);doubley1(doublex);doubleyn(intn,doublex);floaty0f(floatx);floaty1f(floatx);floatynf(intn,floatx);longdoubley0l(longdoublex);longdoubley1l(longdoublex);longdoubleynl(intn,longdoublex);

   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