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# scipy.special.gammainc

`scipy.special.``gammainc`(a, x) = <ufunc 'gammainc'>

  Regularized lower incomplete gamma function.

  Defined as

  \[\frac{1}{\Gamma(a)} \int_0^x t^{a - 1}e^{-t} dt\]

  for \(a > 0\) and \(x \geq 0\). The function satisfies the relation `gammainc(a, x) + gammaincc(a, x) = 1` where `gammaincc` is the regularized upper incomplete gamma function.

  See also

  `gammaincc`
    regularized upper incomplete gamma function
  `gammaincinv`
    inverse to `gammainc` versus `x`
  `gammainccinv`
    inverse to `gammaincc` versus `x`

  Notes

  The implementation largely follows that of [R421].

  References

  [R421] | (1, 2) Maddock et. al., “Incomplete Gamma Functions”, http://www.boost.org/doc/libs/1_61_0/libs/math/doc/html/math_toolkit/sf_gamma/igamma.html