# flapjackery

less info
reputation
411
bio website location age member for 2 years, 8 months seen 10 hours ago profile views 210

# 19 Revisions

 1d revised Sequence of $f_n \in R[0, 1]$ that converges pointwise to $f \in R[0, 1]$ such that $\lim_{n \to \infty} \int_0^1 f_n dx \neq \int_0^1 f dx$. added 32 characters in body; edited tags Nov20 revised For what values $q,r$ does the improper integral $\int_0^1 x^q (1-x^2)^r dx$ converge? deleted 29 characters in body Nov20 revised For what values $q,r$ does the improper integral $\int_0^1 x^q (1-x^2)^r dx$ converge? edited body Nov20 revised For what values $q,r$ does the improper integral $\int_0^1 x^q (1-x^2)^r dx$ converge? edited tags Nov15 revised Compute $\sum_{n=0}^\infty \frac{(-1)^n}{(2n+1)^3} = \frac{\pi^3}{32}$ using residue theory. added 144 characters in body Oct15 revised Evaluate $\int_{\partial C} \frac{dz}{(z-a)(z-b)}$ where $\partial C$ is the boundary of a rectangle ($a$ and $b$ are not on $\partial C$) There's more than my suggested ways of looking at the points a and b. See answers. Oct10 revised Show $f(z) = \frac{z}{e^z-1}$ is analytic in the neighborhood of the origin and find the first 4 terms in its power series representation added 160 characters in body Oct2 revised Prove that $\sum_0^\infty \frac{z^n}{1-z^{2n}}$ converges for all $\left|z\right|<1$ and $\left|z\right|>1$. edited body Sep30 revised Let $u(x,y) = x^2 + 2axy + by^2$, where $a$ and $b$ are real, when is $u$ the real part of an analytic function and what's the imaginary part? added 884 characters in body Sep30 revised (complex variables) Expand $\frac{2z+3}{1+z}$ in a power series of $z-1$ and comment on its convergence added 9 characters in body; edited title Sep26 revised When is the conjugate of an analytic complex function analytic also? edited title Sep25 revised Prove the existence of a greatest lower bound of $X$ if $X \subset \mathbb{R}$ is a non-empty set that is bounded below deleted 22 characters in body Sep24 revised (complex variables) Show that a convergent sequence in the plane means that the corresponding points of the sequence on the Riemann sphere converges added 121 characters in body Sep24 revised Given the sets $X$ and $Y$ in the real numbers with least upper bounds $a$ and $b$ respectively, prove that $a+b$ is the least upper bound for $X + Y$ added 6 characters in body Sep21 revised (complex variables) Express $\cos3\phi$, $\cos4\phi$, and $\cos5\phi$ in terms of $\cos\phi$ and $\sin\phi$. edited body Sep21 revised (complex variables) Express $\cos3\phi$, $\cos4\phi$, and $\cos5\phi$ in terms of $\cos\phi$ and $\sin\phi$. deleted 21 characters in body May15 revised Does a quadratic necessarily have a root in this interval? deleted 35 characters in body Mar9 revised Proof involving matrix inverse of: $\|A^{-1}\|_\infty \ge \frac{\|U^{-1}\|_\infty}{n}$ deleted 266 characters in body Mar9 revised Proof involving matrix inverse of: $\|A^{-1}\|_\infty \ge \frac{\|U^{-1}\|_\infty}{n}$ added 61 characters in body