bessel_y1_real_vectorreturns an array of values of the Bessel function .
For full information please refer to the NAG Library document for s17ar
- xfloat, array-like, shape
The argument of the function, for .
- ffloat, ndarray, shape
, the function values.
- ivalidint, ndarray, shape
contains the error code for , for .
On entry, is too large. contains the amplitude of the oscillation, .
On entry, , is undefined. contains .
is too close to zero, there is a danger of overflow. On failure, contains the value of at the smallest valid argument.
- (errno )
On entry, .
- (errno )
On entry, at least one value of was invalid.
Check for more information.
bessel_y1_real_vectorevaluates an approximation to the Bessel function of the second kind for an array of arguments , for .
Note: is undefined for and the function will fail for such arguments.
The function is based on four Chebyshev expansions:
and , with .
For near zero, . This approximation is used when is sufficiently small for the result to be correct to machine precision. For extremely small , there is a danger of overflow in calculating and for such arguments the function will fail.
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