# 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

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 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.

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