Complex Complete Beta Function

The Complete Beta function BetaC(x, y) = Gam(x) * Gam(y) / Gam(x+y). This is computed by:

If x.i == 0 and y.i == 0, use the real BetaC(x.r, y.r) function.

See: Real Complete Beta Function

Else if (Gam(x) is not infinite) and (Gam(y) is not infinite) and Gam(x+y) is infinite, then BetaC(x, y) = 0. Note, Gam(x) is infinite iff x is a real integer <= 0.

Else if (((Gam(x) is infinite) or (Gam(y) is infinite)) and (Gam(x+y) is not infinite)) or ((Gam(x) is infinite) and (Gam(y) is infinite)), then Error, BetaC(x, y) is infinite.

Else BetaC(x, y) = 1 / (x * Bino(x+y−1, y−1).

See: Beta Function -- From MathWorld
And: Wolfram Function Evaluation -- Beta[a, b]

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