Complex GamL(a, x) = Lower Incomplete Gamma Function


If a == 0 and x == 0, GamL(0, 0) = 0.

Else if a is a real integer <= zero, "Cannot take GamL(a, x) if a is an integer <= zero, except GamL(0, 0) = 0".

Else if x == 0, GamL(a, 0) = 0 if a is not a negative real integer.

Else if a.i == 0 and x.i == 0 and x.r >= 0, use the real GamL(a.r, x.r) function.

See: Real GamL(a, x) = Lower Incomplete Gamma Function

Else if a is a real integer <= zero, "Cannot take GamL(a, x) if a is an integer <= zero, except GamL(0, 0) = 0"

Else if x < a + 1 or x.r < 100, compute GamL(a, x) by series.

Else compute GamU(a, x) by continued fraction, GamL(a, x) = Gam(a) − GamU(a, x).

See: Incomplete Gamma Function -- From MathWorld
And: Wolfram Function Evaluation -- Gamma3 (GamL(a, x) = Gamma[a, 0, x])

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Changes last made on Monday, 06-Aug-07 16:15:40 PDT

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