On defining the incomplete gamma function
The incomplete Gamma function γ(α, x+) is defined as locally summable function on the real line for α > 0 by γ(α,x+)= ∫0x+ uα-1e-udu, the integral diverging for α ≤ 0. The incomplete Gamma function can be defined as a distribution for α< 0 and α ≠ -1, - 2,... by using the recurrence formula γ(...
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| Main Authors: | , , |
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| Format: | Article |
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Taylor and Francis Group
2003
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| Online Access: | http://psasir.upm.edu.my/id/eprint/112985/ https://www.tandfonline.com/doi/abs/10.1080/1065246031000081667 |
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| Summary: | The incomplete Gamma function γ(α, x+) is defined as locally summable function on the real line for α > 0 by γ(α,x+)= ∫0x+ uα-1e-udu, the integral diverging for α ≤ 0. The incomplete Gamma function can be defined as a distribution for α< 0 and α ≠ -1, - 2,... by using the recurrence formula γ(α + 1, x+) = αγ(α x+) - x+αe-x. In the following, we define the distribution γ(-m, x+) for m = 0, 1, 2, .... |
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