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...Contents thegammafunction existence of s thefunctional equation thefactorial function and special values thebetafunctionandthegammafunction stirling formula probabilities convergence series fromstirling to the central limit theorem integral test poor man elementary approaches towards stationary phase thecentral gamma in this chapter we ll explore some strange wonderful properties dened by for or actually is z x xdx e dx therearecountlessintegralsorfunctionswecandene justlookingatit thereisnothingtomake you think it will appear throughout probability statistics but does see where occurs why discuss many its most important looking at denition natural ask do have re strictions on whenever are given an integrand must make sure well behaved before can conclude exists frequently there two trouble points check near okay three example consider f interval deniteness let then blows up theargumentsabovecan andshould beusedeverytimeyoumeetanintegral eventhoughour analysis hasn t suggested a reason...