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 Searching for an asymptotic to exp[0.5] tommy1729 Ultimate Fellow Posts: 1,491 Threads: 355 Joined: Feb 2009 09/16/2021, 11:13 PM - quote - As a small example :  integral from 1 to +oo [ t^x g(t) dt ] with g(t) = exp(- ln(t)^2 )  equals : (1/2) * ( erf((x+1)/2) +1) *  sqrt(pi) * exp( (1/4)* (x+1)^2 ). I find this fascinating. - end quote - another useful example is   integral from 1 to +oo [ t^x g(t) dt ] with g(t) = ln(t)^v  equals : v! (x-1)^(-v-1) for Re(x)>1. thereby connecting to laurent series and more. This might be well known but for completeness and relevance I had to add it. regards tommy1729 « Next Oldest | Next Newest »

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