I want to understand how to calculate the integrals in the picture. gamma is the Euler Macheroni constant and corresponds to the integral from 0 to infinity of exp(-u) log(u) du
#Exponential integral
sharp wedge
hollow moss
So the issue is the extra u factor? If so, I think you can just do integration by parts
sharp wedge
the lower limits leads to blowing up the log, therefore I can not do partial integration
trim raven
nah partial doesn't really work, we need something beautiful for this
I'm trying feynmans rn
see where i can get
trim raven
nah partial doesn't really work, we need something beautiful for this
because it's pretty obvious we have to end up with the integral for euler macaroni constant
sharp wedge
Feynman works thank you!!
sharp wedge
whats so incredible about it?
sharp wedge
So I did e^(alpha u ) for Feynman, I guess you did sth else to obtain the digamma
Can you share?
What I found fun is that this implies that exp(-u) (u-1) log(u) is a probability density
sharp wedge
nice so much unrevealed
trim raven
What I found fun is that this implies that exp(-u) (u-1) log(u) is a probability...
oh that is nice also
sharp wedge
Yes more generally up to a prefactor exp(-u) (u^k- k!) log(u) yields a density