Psi (polygamma) function
Y = psi(X)
Y = psi(k,X)
Y = psi(X) evaluates the ψ function
for each element of array X. X must
be real and nonnegative. The ψ function,
also known as the digamma function, is the logarithmic derivative
of the gamma function
Y = psi(k,X) evaluates
the kth derivative of ψ at
the elements of X. psi(0,X) is
the digamma function, psi(1,X) is the trigamma
function, psi(2,X) is the tetragamma function,
etc.
Use the psi function to calculate Euler's
constant, γ.
format long -psi(1) ans = 0.57721566490153 -psi(0,1) ans = 0.57721566490153
The trigamma function of 2, psi(1,2), is
the same as (π2/6) – 1.
format long psi(1,2) ans = 0.64493406684823 pi^2/6 - 1 ans = 0.64493406684823
[1] Abramowitz, M. and I. A. Stegun, Handbook of Mathematical Functions, Dover Publications, 1965, Sections 6.3 and 6.4.