Psi (Polygamma) Function
Arbitrary order Polygamma function valid in the entire complex plane.
psi(k, z)
k |
order of the polygamma function, whole number greater or equal 0. |
z |
numeric complex number or vector. |
Computes the Polygamma function of arbitrary order, and valid in the entire complex plane. The polygamma function is defined as
ψ(n, z) = \frac{d^{n+1}}{dz^{n+1}} \log(Γ(z))
If n is 0 or absent then psi will be the Digamma function.
If n=1,2,3,4,5 etc. then psi will be the
tri-, tetra-, penta-, hexa-, hepta- etc. gamma function.
Returns a complex number or a vector of complex numbers.
psi(2) - psi(1) # 1
-psi(1) # Eulers constant: 0.57721566490153 [or, -psi(0, 1)]
psi(1, 2) # pi^2/6 - 1 : 0.64493406684823
psi(10, -11.5-0.577007813568142i)
# is near a root of the decagamma functionPlease choose more modern alternatives, such as Google Chrome or Mozilla Firefox.