NAME

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

SYNOPSIS

[XSI] #include <math.h>

double j0(double x);
double j1(double x);
double jn(int n, double x);

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

^[MXX] If x is +Inf, +0 shall be returned.

^[MXX] If x is NaN, a NaN shall be returned.

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.

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.