Question Number 103124 by Faetma last updated on 12/Jul/20

Li(z)=∫_2 ^z (1/(ln t))dt Li(a+ib)=R(∫_2 ^(a+ib) (1/(ln t))dt)+iI(∫_2 ^(a+ib) (1/(ln t))dt) Can you explain me how get the formula for R(Li(z)) and I(Li(z))?

Answered by mathmax by abdo last updated on 13/Jul/20

L_i (z) =∫_2 ^z (dt/(lnt)) we take z =a+ib ⇒L_i (a+ib) =∫_2 ^(a+ib) (dt/(lnt)) this integral is complex so ∃ α and β from R /L_i (a+ib) =α +iβ α =Re(∫_2 ^(a+ib) (dt/(lnt))) and β =Im(∫_2 ^(a+ib) (dt/(lnt))) the problem here is how to find α and β...!

Commented bymathmax by abdo last updated on 13/Jul/20

your cut is crying why...?

Commented byFaetma last updated on 13/Jul/20

Exatly, but I don′t know how can we do that :/