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Searching for an asymptotic to exp[0.5]
- 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
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Messages In This Thread
RE: Searching for an asymptotic to exp[0.5] - by tommy1729 - 09/16/2021, 11:13 PM

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