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
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
