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Thread: residues gamma function(qustion hollywood)

  1. #1
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    residues gamma function(qustion hollywood)

    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
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