GamU(a, x) = Upper Incomplete Gamma Function

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

If x < a + 1 or x < 100,

GamU(a, x) = Gam(a) − GamL(a, x),

where GamL is the Lower incomplete Gamma function. See the GamL(x, y) function.

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

GamU(a, x) = Exp(−x) * x^a * (1/x+ (a−1)/1+ 1/x+ (2−a)/1+ 2/x+ ...)

is used, summed evaluated until the value stops changing. The notation (1/x+ (a−1)/1+ 1/x+ (2−a)/1+ 2/x+ ...) represents a continued fraction development for GamU(a, x) that converges for x > 0.

Cannot take GamU(a, 0) if a is an integer <= zero.

See: Incomplete Gamma Function -- From MathWorld
And: Wolfram Function Evaluation -- Gamma2 (GamU(a, x) = Gamma[a, x])

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