y0 man page

Prolog

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y0, y1, yn — Bessel functions of the second kind

Synopsis

#include <math.h>

double y0(double x);
double y1(double x);
double yn(int n, double x);

Description

The y0(), y1(), and yn() functions shall compute Bessel functions of x of the second kind of orders 0, 1, and n, respectively.

An application wishing to check for error situations should set errno to zero and call feclearexcept(FE_ALL_EXCEPT) before calling these functions. On return, if errno is non-zero or fetestexcept(FE_INVALID | FE_DIVBYZERO | FE_OVERFLOW | FE_UNDERFLOW) is non-zero, an error has occurred.

Return Value

Upon successful completion, these functions shall return the relevant Bessel value of x of the second kind.

If x is NaN, NaN shall be returned.

If the x argument to these functions is negative, -HUGE_VAL or NaN shall be returned, and a domain error may occur.

If x is 0.0, -HUGE_VAL shall be returned and a pole error may occur.

If the correct result would cause underflow, 0.0 shall be returned and a range error may occur.

If the correct result would cause overflow, -HUGE_VAL or 0.0 shall be returned and a range error may occur.

Errors

These functions may fail if:

Domain Error

The value of x is negative.

If the integer expression (math_errhandling & MATH_ERRNO) is non-zero, then errno shall be set to [EDOM]. If the integer expression (math_errhandling & MATH_ERREXCEPT) is non-zero, then the invalid floating-point exception shall be raised.

Pole Error

The value of x is zero.

If the integer expression (math_errhandling & MATH_ERRNO) is non-zero, then errno shall be set to [ERANGE]. If the integer expression (math_errhandling & MATH_ERREXCEPT) is non-zero, then the divide-by-zero floating-point exception shall be raised.

Range Error

The correct result would cause overflow.

If the integer expression (math_errhandling & MATH_ERRNO) is non-zero, then errno shall be set to [ERANGE]. If the integer expression (math_errhandling & MATH_ERREXCEPT) is non-zero, then the overflow floating-point exception shall be raised.

Range Error

The value of x is too large in magnitude, or the correct result would cause underflow.

If the integer expression (math_errhandling & MATH_ERRNO) is non-zero, then errno shall be set to [ERANGE]. If the integer expression (math_errhandling & MATH_ERREXCEPT) is non-zero, then the underflow floating-point exception shall be raised.

The following sections are informative.

Application Usage

On error, the expressions (math_errhandling & MATH_ERRNO) and (math_errhandling & MATH_ERREXCEPT) are independent of each other, but at least one of them must be non-zero.

See Also

feclearexcept(), fetestexcept(), isnan(), j0()

The Base Definitions volume of POSIX.1‐2008, Section 4.19, Treatment of Error Conditions for Mathematical Functions, <math.h>

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2013 IEEE/The Open Group POSIX Programmer's Manual