The Open Group Base Specifications Issue 7
IEEE Std 1003.1-2008, 2016 Edition
Copyright © 2001-2016 The IEEE and The Open Group

#### NAME

> y0, y1, yn - Bessel functions of the second kind

#### SYNOPSIS

> ``[XSI] #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.

> [MXX] 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.

#### EXAMPLES

> None.

#### 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.

#### RATIONALE

> None.

#### FUTURE DIRECTIONS

> None.

#### SEE ALSO

> feclearexcept, fetestexcept, isnan, j0

> XBD Treatment of Error Conditions for Mathematical Functions, <math.h>

#### CHANGE HISTORY

> First released in Issue 1. Derived from Issue 1 of the SVID.

#### Issue 5

> The DESCRIPTION is updated to indicate how an application should check for an error. This text was previously published in the APPLICATION USAGE section.

#### Issue 6

> The normative text is updated to avoid use of the term "must" for application requirements.

> The RETURN VALUE and ERRORS sections are reworked for alignment of the error handling with the ISO/IEC 9899:1999 standard.

> IEEE Std 1003.1-2001/Cor 2-2004, item XSH/TC2/D6/148 is applied, updating the RETURN VALUE and ERRORS sections. The changes are made for consistency with the general rules stated in "Treatment of Error Conditions for Mathematical Functions'' in the Base Definitions volume of POSIX.1-2008.

#### Issue 7

> POSIX.1-2008, Technical Corrigendum 1, XSH/TC1-2008/0746 [68] is applied.

End of informative text.

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