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Apr
2
answered Shouldn't the yellow marked $a_0$ be $a_0+\langle p(x)\rangle?$
Apr
1
revised Proving an inequality on $\sum_{1\leq i,j \leq n} \langle c_i ,c_j \rangle \times \langle l_i ,l_j \rangle$
$$ in titles takes up too much space on the main page
Mar
31
comment Is 91 the only number which is both a centred cube number and a centred hexagon number?
There are definitely finitely many such numbers (by Siegel's theorem...)
Mar
29
comment $v$ is Conjugate Harmonic to $u$ $\implies$ $f = u + iv$ is Analytic (Proof Verification from Ahlfors)
That sounds right (though I don't have a copy of Ahlfors handy to check). You might want to go back and check exactly what Ahlfors is using as a definition of "harmonic conjugate." (I'm actually used to defining $u$ and $v$ to be harmonic conjugate if $u+iv$ is analytic, which would render this whole thing trivial, but the proof you've given suggests that "$u$ and $v$ satisfy the CR equations" is the definition he's using.)
Mar
29
comment $v$ is Conjugate Harmonic to $u$ $\implies$ $f = u + iv$ is Analytic (Proof Verification from Ahlfors)
$v$ is a conjugate harmonic function of $u$ because they satisfy the Cauchy-Riemann equations. Any pair of functions that satisfy the Cauchy-Riemann equations are guaranteed to both be harmonic, so in a sense you're making use of the fact that $u$ and $v$ are harmonic in your question 2 step.
Mar
29
answered $v$ is Conjugate Harmonic to $u$ $\implies$ $f = u + iv$ is Analytic (Proof Verification from Ahlfors)
Mar
29
revised How to prove this integral $I=\int_{0}^{\frac{\pi}{2}}\frac{dx}{1+\sin^2{(\tan{x})}}$
\dfrac in titles takes up too much vertical space
Mar
26
comment How does one solve arbitrary polygons, in the same sense as one solves a triangle?
Intuitively I would expect there to be an algorithm like: 1) if there are any three pieces of data in a row (either angle-side-angle or side-angle-side), you can use them to eliminate a side (possibly multiplying the number of possibilities somewhat); 2) If you've done that as many times as possible and you're still not down to a triangle, there are an infinite number of possibilities. But the case analysis to prove this seems tedious...
Mar
25
answered Prove $\frac{\sin\theta}{1+\cos\theta} + \frac{1+\cos\theta}{\sin\theta} = \frac{2}{\sin\theta}$
Mar
25
answered An “Arbitrary Free Product of Groups”
Mar
24
reviewed Reopen Mathematical function alike to primes
Mar
23
revised Why a unit set is not the same as its element? $\{x\} \ne x$?
fixed some typos
Mar
23
revised Growth rate of $n^{\sin n}$
formatting
Mar
19
reviewed Reopen Why is the statement false: If a test is rejected at significance level α, the probability that the null hypothesis is true equals α?
Mar
19
revised Verify the identity $\sin 3x + \sin x = 4\sin x - 4\sin^3 x$
$$ in titles is unnecessary and wastes space on the main page
Mar
18
comment $3\cos(x+1) =\cos(x+2)$. This is a equation, involving trigonometric functions.
@Sabyasachi: It absolutely does help. The answer isn't entirely simple, but you can make it considerably simpler than Wolfram Alpha makes it out to be.
Mar
18
revised Find the limit $\lim_{n \rightarrow \infty} \frac{2 + (-1)^n}{2^{n+1} + (-1)^{n+1}} $
\displaystyle in titles takes up too much vertical space
Mar
16
revised How find the minimum of $ab+\frac{1}{a^2}+\frac{1}{b^2}$
\dfrac in titles takes up too much vertical space
Mar
12
reviewed No Action Needed Application of the Inverse Function Theorem
Mar
11
revised Prove $ \left |\sin(x) - x + \frac{x^3}{3!} \right | < \frac{4}{15}$
\dfrac in titles takes up too much vertical space