# y0 - Man Page

Bessel functions of the second kind

## Prolog

This manual page is part of the POSIX Programmer's Manual. The Linux implementation of this interface may differ (consult the corresponding Linux manual page for details of Linux behavior), or the interface may not be implemented on Linux.

## Synopsis

#include <math.h> double y0(doublex); double y1(doublex); double yn(intn, doublex);

## 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.*

## 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()

The Base Definitions volume of POSIX.1-2017, *Section 4.20*, *Treatment of Error Conditions for Mathematical Functions*, <math.h>

## Copyright

Portions of this text are reprinted and reproduced in electronic form from IEEE Std 1003.1-2017, Standard for Information Technology -- Portable Operating System Interface (POSIX), The Open Group Base Specifications Issue 7, 2018 Edition, Copyright (C) 2018 by the Institute of Electrical and Electronics Engineers, Inc and The Open Group. In the event of any discrepancy between this version and the original IEEE and The Open Group Standard, the original IEEE and The Open Group Standard is the referee document. The original Standard can be obtained online at http://www.opengroup.org/unix/online.html .

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