Functions {gamma function} can be gamma(n) = (n! * n^z) / (z * (z + 1) * (z + 2) * ... * (z + n)), where n is number. It has limit at infinity. Gamma function is integral {Euler's integral} from t = 0 to t = infinity of t^(z - 1) * e^(-t) * dt. Value at z + 1 is z! = product from i = 1 to i = z of integral from x = 0 to x = 1 of (-log(x))^z * dx.
Functions {psi function} {digamma function} can be derivatives of gamma divided by gamma, so value at z + 1 is value at z plus 1 divided by z: psi(z + 1) = psi(z) + 1/z.
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Date Modified: 2022.0225