GamL(a, x) = Lower Incomplete Gamma Function

GamL(a, x) is the lower incomplete Gamma function with parameter a and argument x. It is defined as the Integral from 0 to x of exp(−t) * t^(a−1) dt (a > 0).

If x < a + 1 or x < 100,

GamL(a, x) = Exp(−x) * Sum[x^n * Gam(a)/Gam(a+1+n)]

is used, summed for n = 0 to when the sum stops changing.

If x >= a + 1 and x >= 100,

GamL(a, x) = Gam(a) − GamU(a, x),

where GamU is the upper incomplete Gamma function. See the GamU(a, x) function.

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

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 20:47:18 PDT