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


The argument of the function.


The index of the first member of the sequence of functions.


The number of members required in the sequence , for .

ansfloat, ndarray, shape

The first elements of contain the required values , for .

(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.


polygamma_deriv computes values of the function

for , , , 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.


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