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The definition of analytic continuation of holomorphic function is stated as follows:Let $f_{1}$ and $f_{2}$ be two analytic functions on two domains (open and connected) $Omega_{1}$ and...
Asked on 01/29/2021
1 answerI am having trouble proving the following statement, which at first seemed intuitively true to me. Let $S$ be a surface in $mathbb{R}^{3}$. Suppose that there is a...
Asked on 01/29/2021 by MK7
1 answerHow to solve $sqrt{x!y!}=xy$ for $(x,y)inmathbb{Z}_{geq0}timesmathbb{Z}_{geq0}$?In this task they are asking to find ordered pair couple in $mathbb{Z}$ that satisfies the above equation,So that, i started...
Asked on 01/29/2021 by Ramez Hindi
3 answerConsider the localization of $R = mathbb Z/10mathbb Z$ at $6$. We use the multiplicative subset $S = { 1, 6 }$. we build fractions of the...
Asked on 01/29/2021 by Siddharth Bhat
1 answerThis particular question is from Ponnusamy Silvermann complex section 9.22 ( question no. 2) and I am unable to solve it.Let f(z) be analytic in deleted neighborhood of origin and...
Asked on 01/29/2021
2 answerI am studying the topic of torsion and curvature and I ran into the following problem: Consider the helix $alpha(t)=(asin t,acos t,bt)$. Get the relationship between constantsso that...
Asked on 01/28/2021
1 answerI want prove that, for $ninmathbb{N}$ and$rho > 1$:$$int_{0}^{pi}!!!frac{sin^{n - 2,}left(thetaright)}{left[rho^{2} - 2rhocosleft(thetaright) + 1right]^{n/2},},mathrm{d}theta =frac{1}{rho^{n - 2}left(rho^2-1right)}int_{0}^{pi}!!!sin^{n - 2}left(thetaright)...
Asked on 01/28/2021 by inoc
1 answerThe problem is as follows: Let $S^{circ}$, $C^{g}$ and $R,textrm{rad}$ the measures of a positive angle in sexagesimal, centesimal and radian degrees respectively such as: $$E^{circ}=frac{5S^g}{162}+frac{C^circ}{50}+frac{2pi^2}{360R}textrm{rad}$$...
Asked on 01/28/2021 by Chris Steinbeck Bell
1 answerSuppose there are two functions $f: X to Y$ and $g: X to Y$. In what sense do we say $f = g$? In my understanding, the...
Asked on 01/28/2021 by Ziqi Fan
0 answerI am unsure of this derivative. The answer should apparently be $frac{-a}{xsqrt{x^2-a^2}}$ by using the chain rule. However I arrived at a slightly different answer using implicit diff of...
Asked on 01/28/2021 by Fady
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