3.5.1.3.61 Real_polygamma

Definition:

\(psi\_deriv =real\_polygamma(x,k)\) evaluates an approximation to the kth derivative of the psi function \(\psi (x)\) by

\[\Psi ^k(x)=\frac{d^k}{dx^k}\Psi (x)=\frac{d^k}{dx^k}(\frac d{dx}\log _e\Gamma (x))\]

where x is real with x≠0, -1, -2, ... and k=0,1,......6.

For more information please review the s14aec function in the NAG document.

Parameters:

x (input, double)

The argument x of the function.

Constraint: x must not be 'too close' to a non-positive integer.

k (input, double)

The argument k of the function.

Constraint: 0≤k≤6

\(psi\_deri\) (output, double)

Approximation to the kth derivative of the psi function \(\psi (x)\).