d-dx-of-x- Tinku Tara June 4, 2023 None 0 Comments FacebookTweetPin Question Number 145197 by Gbenga last updated on 03/Jul/21 d/dxofx!=? Commented by Dwaipayan Shikari last updated on 03/Jul/21 x!=Γ(x+1)dx!dx=Γ′(x+1)=Γ(x+1)ψ(x+1)AsΓ′(x+1)Γ(x+1)=ψ(x+1) Answered by puissant last updated on 03/Jul/21 Γ(x)=(x−1)!=∫0+∞tx−1e−tdt1Γ(x)=xeγx∏∞k=1(1+xk)e−xkln(1Γ(x))=−ln(Γ(x))=ln(x)+γx+∑∞k=1(1+xk)−xkddx(ln(1Γ(x)))=−(ln(Γ(x)))′=−Γ′(x)Γ(x)=1x+γ+∑∞k=111+xk×1k−1k=−1x−γ+∑∞k=11k−1x+kλ(x)=−γ+∑∞k=11k−1k−1+x⇒λ(x+1)=−γ+∑∞k=11k−1k+x⇒ddx(x!)=Γ′(x+1)Γ(x+1)…. Terms of Service Privacy Policy Contact: info@tinkutara.com FacebookTweetPin Post navigation Previous Previous post: Let-a-b-c-0-c-3-a-b-3-0-and-a-2-b-2-c-2-3-Prove-that-1-2-a-3-b-c-3-b-3-c-a-3-c-3-a-b-3-2-Determine-when-equality-holds-Next Next post: How-to-find-maximum-value-of-k-if-5-cos-2-sin-2k-0-pi- Leave a Reply Cancel replyYour email address will not be published.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.