$jn()

Synopsis

$jn(<level> <number>)

Technical

Returns the Bessel function of the first kind of integer order <level> evaluated at <number>, using the C library's jn(level, number). Both arguments are required; omitting either returns the empty string. Additional arguments are ignored.

The order uses base-detecting integer conversion, accepting decimal, hexadecimal, and leading-zero octal, then is stored as a C int. Keep it within that type's range. The number uses atof, accepting decimal fractions and scientific notation. Nonnumeric arguments convert to zero, and numeric prefixes can be accepted despite trailing text. Negative orders and arguments are passed to the library without an EPIC restriction.

The calculation uses a C double. Results are formatted with %.50g, not limited to six decimal places; extra digits do not imply 50 digits of accuracy. The floating_point_math and floating_point_precision settings do not change this calculation or formatting.

Returns

The calculated Bessel value when errno is zero, DOM for EDOM, RANGE for ERANGE, or the empty string for another reported error. Unlike the unary math wrapper, this wrapper clears errno before argument conversion, so conversion errors can also affect the result.

EPIC checks errno, not floating-point exception flags. Large arguments or underflow can produce a library range error; the exact error reporting is platform-dependent. See the POSIX jn specification. This function is registered unconditionally and requires the platform math library's jn implementation.

Examples

The approximate example describes the numeric value; the returned string may contain more digits. For the Bessel function of the second kind, see yn.

Source

Registration, MATH_FUNCTION2, and MATH_RETVAL are in source/functions.c. Argument conversion and floating-point return formatting are in include/functions.h.