The Open Group Base Specifications Issue 8
IEEE Std 1003.1-2024
Copyright © 2001-2024 The IEEE and The Open Group

NAME

j0, j1, jn — Bessel functions of the first kind

SYNOPSIS

[XSI] [Option Start] #include <math.h>

double j0(double
x);
double j1(double
x);
double jn(int
n, double x); [Option End]

DESCRIPTION

The j0(), j1(), and jn() functions shall compute Bessel functions of x of the first 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 first kind.

If the x argument is finite and too large in magnitude, or the correct result would cause underflow [MXX] [Option Start]  and is not representable, [Option End] a range error may occur, and the function shall return [MXX] [Option Start]  0.0, or [Option End] (if the IEC 60559 Floating-Point option is not supported) an implementation-defined value no greater in magnitude than DBL_MIN.
[MXX] [Option Start] If the correct result would cause underflow, and is representable, a range error may occur and the correct value shall be returned. [Option End]

[MXX] [Option Start] If x is +Inf, +0 shall be returned. [Option End]

[MXX] [Option Start] If x is NaN, a NaN shall be returned. [Option End]

ERRORS

These functions may fail if:

Range Error
The value of x was too large in magnitude, or an underflow occurred.

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.

No other errors shall occur.


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 , y0

XBD 4.23 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 may fail [EDOM] error is removed for the case for NaN.

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

Issue 7

POSIX.1-2008, Technical Corrigendum 1, XSH/TC1-2008/0350 [68] is applied.

Issue 8

Austin Group Defect 714 is applied, changing the behavior of these functions for special cases to be a better match for their mathematical behavior.

End of informative text.

 

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