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 :/