When and , the absolute value of the last integral is smaller than . By choosing a large enough , this last expression can be made smaller than for any desired value . Thus, the gamma function can be evaluated to bits of precision with the above series.
whEN aNd , The abSOlute vALue of THe lAst integraL is sMallEr tHAn . by chooSing a laRge eNough , tHis lasT expRession can bE mADE smaller tHan for any dEsiREd ValuE . ThuS, thE gammA fuNctIOn can Be EvalUated to BITs of pREcIsion WITH tHe abOve Series.