bessel_j0_realreturns the value of the Bessel function .
For full information please refer to the NAG Library document for s17ae
The argument of the function.
The value of the Bessel function .
- (errno )
On entry, .
is too large, the function returns the amplitude of the oscillation, .
bessel_j0_realevaluates an approximation to the Bessel function of the first kind .
Note: , so the approximation need only consider .
The function is based on three Chebyshev expansions:
For near zero, . This approximation is used when is sufficiently small for the result to be correct to machine precision.
For very large , it becomes impossible to provide results with any reasonable accuracy (see Accuracy), hence the function fails. Such arguments contain insufficient information to determine the phase of oscillation of ; only the amplitude, , can be determined and this is returned on failure. The range for which this occurs is roughly related to machine precision; the function will fail if .
NIST Digital Library of Mathematical Functions
Clenshaw, C W, 1962, Chebyshev Series for Mathematical Functions, Mathematical tables, HMSO