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1d
revised Sequence of $f_n \in R[0, 1]$ that converges pointwise to $f \in R[0, 1]$ such that $\lim_{n \to \infty} \int_0^1 f_n dx \neq \int_0^1 f dx$.
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Nov
20
revised For what values $q,r$ does the improper integral $\int_0^1 x^q (1-x^2)^r dx$ converge?
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Nov
20
revised For what values $q,r$ does the improper integral $\int_0^1 x^q (1-x^2)^r dx$ converge?
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Nov
20
revised For what values $q,r$ does the improper integral $\int_0^1 x^q (1-x^2)^r dx$ converge?
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Nov
15
revised Compute $\sum_{n=0}^\infty \frac{(-1)^n}{(2n+1)^3} = \frac{\pi^3}{32}$ using residue theory.
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Oct
15
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.
Oct
10
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
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Oct
2
revised Prove that $\sum_0^\infty \frac{z^n}{1-z^{2n}}$ converges for all $\left|z\right|<1$ and $\left|z\right|>1$.
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Sep
30
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?
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Sep
30
revised (complex variables) Expand $\frac{2z+3}{1+z}$ in a power series of $z-1$ and comment on its convergence
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Sep
26
revised When is the conjugate of an analytic complex function analytic also?
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Sep
25
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
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Sep
24
revised (complex variables) Show that a convergent sequence in the plane means that the corresponding points of the sequence on the Riemann sphere converges
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Sep
24
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 $X + Y$
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Sep
21
revised (complex variables) Express $\cos3\phi$, $\cos4\phi$, and $\cos5\phi$ in terms of $\cos\phi$ and $\sin\phi$.
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Sep
21
revised (complex variables) Express $\cos3\phi$, $\cos4\phi$, and $\cos5\phi$ in terms of $\cos\phi$ and $\sin\phi$.
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May
15
revised Does a quadratic necessarily have a root in this interval?
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Mar
9
revised Proof involving matrix inverse of: $\|A^{-1}\|_\infty \ge \frac{\|U^{-1}\|_\infty}{n}$
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Mar
9
revised Proof involving matrix inverse of: $\|A^{-1}\|_\infty \ge \frac{\|U^{-1}\|_\infty}{n}$
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