naginterfaces.library.specfun.polygamma_deriv¶
- naginterfaces.library.specfun.polygamma_deriv(x, n, m)[source]¶
polygamma_deriv
returns a sequence of values of scaled derivatives of the psi function (also known as the digamma function).For full information please refer to the NAG Library document for s14ad
https://support.nag.com/numeric/nl/nagdoc_30.2/flhtml/s/s14adf.html
- Parameters
- xfloat
The argument of the function.
- nint
The index of the first member of the sequence of functions.
- mint
The number of members required in the sequence , for .
- Returns
- ansfloat, ndarray, shape
The first elements of contain the required values , for .
- Raises
- NagValueError
- (errno )
On entry, .
Constraint: .
- (errno )
On entry, .
Constraint: .
- (errno )
On entry, .
Constraint: .
- (errno )
Computation abandoned due to the likelihood of underflow.
- (errno )
Computation abandoned due to the likelihood of overflow.
- (errno )
There is not enough internal workspace to continue computation. is probably too large.
- Notes
polygamma_deriv
computes values of the functionfor , , , where is the psi function
and denotes the th derivative of .
The function is derived from the function PSIFN in Amos (1983). The basic method of evaluation of is the asymptotic series
for large greater than a machine-dependent value , followed by backward recurrence using
for smaller values of , where when , when , and , , are the Bernoulli numbers.
When is large, the above procedure may be inefficient, and the expansion
which converges rapidly for large , is used instead.
- References
NIST Digital Library of Mathematical Functions
Amos, D E, 1983, Algorithm 610: A portable FORTRAN subroutine for derivatives of the psi function, ACM Trans. Math. Software (9), 494–502