yn

Return the Bessel function of the second kind for an integer order.

Synopsis

$yn(<level> <number>)

Technical

Returns the Bessel function of the second kind of order level, evaluated at number, using the platform math library's yn(level, number). Both arguments are required; omitting either returns an empty string. Additional arguments are ignored. For the first-kind function, see jn.

The order uses base-zero integer conversion and is stored in a C int. The number uses atof, accepting decimal fractions and scientific notation. Nonnumeric text converts to zero, and numeric prefixes can be accepted despite trailing text. Keep the order within C int range. Negative orders are passed through to the library; there is no EPIC-side domain validation.

The ordinary real-valued domain is positive number. Zero is a pole and negative arguments cause a domain error. Error reporting, overflow, underflow, and special-value handling depend on the platform library; see the Linux yn manual. EPIC does not independently reject these inputs.

Results use C double and are formatted with %.50g, rather than being limited to six decimal places. The extra printed digits do not imply 50 digits of accuracy. The floating_point_math and floating_point_precision settings do not control this calculation or formatting.

Returns

The calculated value when errno is zero, DOM when it is EDOM, RANGE when it is ERANGE, or an empty string for another error. The wrapper clears errno before argument conversion, so conversion errors can affect the final result as well as library calculation errors.

EPIC checks errno, rather than floating-point exception flags. If the library reports a special value without setting errno, that value is formatted instead of producing an error word. The function is registered unconditionally and requires the platform math library's yn implementation.

Examples

The approximate examples describe numeric values; the returned strings may contain more digits.

Source

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