Manpages - y0.3

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);

Link with -lm.

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

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.

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 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.

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

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.

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

*j0*(3)

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