trigamma
Computes the trigamma function at x.
The trigamma function is the second derivative of ln(Gamma(x)), or equivalently the derivative of the digamma function: psi'(x) = d/dx psi(x). It appears in the variance of sufficient statistics for exponential-family distributions and in Newton-Raphson updates for maximum-likelihood estimation.
Uses the asymptotic expansion for x >= 8, with recurrence relation to shift smaller arguments upward, and a reflection formula for negative non-integer arguments.
Example:
trigamma(1.0) // 1.6449... (pi^2/6)
trigamma(0.5) // 4.9348... (pi^2/2)
trigamma(2.0) // 0.6449... (pi^2/6 - 1)Content copied to clipboard
Return
the value of the trigamma function at x.
Parameters
x
the point at which to evaluate. Must not be zero or a negative integer (poles of the gamma function).
Throws
if x is zero or a negative integer.