Hi,

here the whole exercise of the residues of gamma function.

I tried a substitution to get the residues:

let 1-s=2u :s=1-2u :s=1 -> u=0

s/2=(1/2-u) :-s/2=(u-1/2) 1-s)/2=u so we have

[R^(u-1/2)*gamma(1/2-u)*gamma(u)]/2u

Then I change gamma u in the numerator gamma(u+1)=u*gamma(u)or gamma(u)=gamma(u+1)/u

so numerator the same but the denominator is now /2u^2 double pole.

for the residue I diff.this expression and then lim u->0(use of formule for residue)

Ik have the same result as in the Pdf file with the only difference the denominator is multiplied by a factor 2.

I have lof R/4sqrt(R) + log 2/2sqrt(R)

Thank you