prove-that-1-4-2pi-3-56-3- Tinku Tara June 4, 2023 Differentiation 0 Comments FacebookTweetPin Question Number 162377 by mnjuly1970 last updated on 29/Dec/21 provethatψ″(14)=−2π3−56ζ(3) Commented by aleks041103 last updated on 29/Dec/21 ψ″(14)=ψ2(14)=(−1)2+12!∑∞k=01(k+14)2+1==−2∑∞k=01(k+14)3=−128∑∞k=01(4k+1)3 Commented by amin96 last updated on 29/Dec/21 bravo Answered by mindispower last updated on 30/Dec/21 Ψ″(14)=−128∑n⩾01(4n+1)3Ψ″(x)−Ψ″(1−x)=−2π3(1+cot2(πx))cot(πx)Ψ″(14)−Ψ″(34)=−4π3ζ(3)=∑n⩾01(4n+1)3+(14n+3)3+164(n+1)3+18(2n+1)3=−Ψ″(14)+Ψ″(34)64+18(18ζ(3)+78ζ(3))Ψ″(34)=Ψ″(14)+4π3⇒−2Ψ″(14)+4π364+ζ(3)8=ζ(3)⇒Ψ″(14)=−56ζ(3)−2π Terms of Service Privacy Policy Contact: info@tinkutara.com FacebookTweetPin Post navigation Previous Previous post: Complete-the-square-in-y-2-8y-9k-and-hence-find-the-value-of-k-that-makes-it-a-perfect-square-Next Next post: Question-162382 Leave a Reply Cancel replyYour email address will not be published.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.