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== Approximation ==
To compute the branches of the inverse gamma function one can first compute the [[Taylor series]] of <math>\Gamma(x)</math> near <math>\alpha</math>. The series can then be truncated and inverted, which yields successively better approximations to <math>\Gamma^{-1}(x)</math>. For instance, we have the quadratic approximation:<ref>{{cite conference |first1=Robert M.|last1=Corless |first2=Folitse Komla|last2=Amenyou |last3=Jeffrey |first3=David |book-title=2017 19th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing (SYNASC) |title=Properties and Computation of the Functional Inverse of Gamma |conference=International Symposium on Symbolic and Numeric Algorithms for Scientific Computing (SYNASC) |date=2017 |pages=65 |doi=10.1109/SYNASC.2017.00020|isbn=978-1-5386-2626-9 |s2cid=53287687 }}</ref>
<math display="block"> \Gamma^{-1}\left(x\right)\approx\alpha+\sqrt{\frac{2\left(x-\Gamma\left(\alpha\right)\right)}{\Psi\left(1,\ \alpha\right)\Gamma\left(\alpha\right)}}.</math>
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