let-f-z-sin-z-z-2-calculate-Res-f-0- Tinku Tara June 4, 2023 Integration 0 Comments FacebookTweetPin Question Number 63031 by mathmax by abdo last updated on 28/Jun/19 letf(z)=sin(z)z2calculateRes(f,0) Commented by mathmax by abdo last updated on 28/Jun/19 0isadoublepole⇒Res(f,0)=limz→01(2−1)!{z2f(z)}(1)=limz→0{sinz}(1)=limz→0cosz=1 Commented by mathmax by abdo last updated on 28/Jun/19 anotherwayiff(z)=∑k=0∞ak(z−z0)k+∑k=1∞a−k(z−z0)−k(tbelaurentserieoff(z))→Res(f,z0)=a−1=coefficientof1z−zointhisseriesowehavesin(z)=∑n=0∞(−1)nz2n+1(2n+1)!=z−z33!+z55!−….⇒sinzz2=1z−z3!+z35!−….⇒Re(f,0)=1(coefficentof1z). Terms of Service Privacy Policy Contact: info@tinkutara.com FacebookTweetPin Post navigation Previous Previous post: nice-calculus-prove-that-0-sin-x-2-sin-x-2-dx-1-4-pi-2-e-2-sin-2-cos-2-Next Next post: let-f-z-1-sin-piz-calculate-Res-f-n-with-n-integr- Leave a Reply Cancel replyYour email address will not be published. Required fields are marked *Comment * Name * Save my name, email, and website in this browser for the next time I comment.