Category: Arithmetic

Question Number 98434 by  M±th+et+s last updated on 14/Jun/20 $$provethat$$$$\mathrm{\Omega }=\underset{n=0}{\sum ^{+\mathrm{\infty }}}\underset{m=0}{\sum ^{+\mathrm{\infty }}}\frac{\mathrm{\Gamma }(n+\frac{1}{2}).\mathrm{\Gamma }(m+\frac{1}{2})}{\mathrm{\Gamma }(n+1).\mathrm{\Gamma }(m+1)}.\frac{{\left(\frac{2}{3}\right)}^n.{\left(\frac{1}{2}\right)}^m}{(n+m+\frac{1}{2})}$$$$=\frac{\sqrt{\mathrm{3}}}{\mathrm{2}\sqrt{\mathrm{2}}}.{G}_{\mathrm{2},\mathrm{2}} ^{\mathrm{2},\mathrm{2}} \left(\frac{\mathrm{1}}{\mathrm{4}}\mid_{\mathrm{0}\:\:,\:\mathrm{0}} ^{\frac{\mathrm{1}}{\mathrm{2}},\frac{\mathrm{1}}{\mathrm{2}}} \right) \…

Question Number 98309 by Rio Michael last updated on 12/Jun/20 $$\mathrm{let}f\left(x\right)=\ln (1+\cosh 2x)$$$$\mathrm{show}\mathrm{that}\underset{x\to \mathrm{\infty }}{\lim }f\left(x\right)=2x-\ln 2$$$$\mathrm{hence}\mathrm{deduce}\underset{x\to -\mathrm{\infty }}{\lim }f\left(x\right)\mathrm{with}\mathrm{the}\mathrm{asympotes}\mathrm{of}\mathrm{the}$$$$\mathrm{curve}.$$ Answered by abdomathmax last…

Question Number 32755 by 7991 last updated on 01/Apr/18 $$\underset{n=1}{\sum ^{\mathrm{\infty }}}\frac{1}{n^2}=\dots .???$$ Commented by Rio Mike last updated on 01/Apr/18 $$\mathrm{solution} \…

Question Number 163687 by gbanda95 last updated on 09/Jan/22 Terms of Service Privacy Policy Contact: info@tinkutara.com

Question Number 98135 by Tony Lin last updated on 11/Jun/20 $$howtosplit{x}^2+xy+y^{2}into$$$$\frac{\sqrt{3}}{2}{(x+y)}^2+\frac{1}{2}{(x-y)}^2?$$ Commented by MJS last updated on…