bio  website  math.ubc.ca/~israel 

location  Vancouver BC  
age  64  
visits  member for  4 years 
seen  7 hours ago  
stats  profile views  5,489 
Associate Professor Emeritus, University of British Columbia, and Optimization Algorithms Researcher, DWave Systems, Burnaby BC
12h

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“Epicycles” (Ptolemy style) in math theory?
For a discussion of epicycles as trigonometric series, see Shlomo Sternberg, "Celestial Mechanics vol. 1", W. A. Benjamin, 1969. 
15h

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“Epicycles” (Ptolemy style) in math theory?
You can see Stokes's original formulation (due to Kelvin) at <books.google.ca/…;. It precedes vector calculus (as formulated by Gibbs et al) by about 50 years. 
19h

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Consecutive numbers with mutually distinct exponents in their canonical prime factorization
Another $5$: $1431124, 1431125, 1431126, 1431127, 1431128$. 
19h

awarded  Good Answer 
20h

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Consecutive numbers with mutually distinct exponents in their canonical prime factorization
You might also mention $1,2,3,4,5$ and $241, 242, 243, 244, 245$. Those and the ones you listed are all the $5$'s less than $10^6$, and there are no sequences of length $>5$ in this range. 
1d

answered  Proof that no differentiable spacefilling curve exists 
Mar 28 
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How to prove that $(1x)^b$ $_2F_1(a,b;c;x)$ can be approximated to $1\alpha x$ (with $\alpha \approx 1$) for $x\ll 1$ in this specific case
That's a series in powers of $x/(x1)$. And what do you get when you express it as a series in powers of $x$? 
Mar 27 
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Variance under timescaling of sample measurements
Of course, a normal random variable doesn't really make sense here, since $X$ is supposed to be nonnegative integervalued. The question is what model the normal distribution is supposed to be approximating. A more usual model for this sort of thing would be a Poisson process, but that would have mean and variance equal (and proportional to the duration of the interval). It should be up to the authors to specify what model is being used here. 
Mar 27 
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How to prove that $(1x)^b$ $_2F_1(a,b;c;x)$ can be approximated to $1\alpha x$ (with $\alpha \approx 1$) for $x\ll 1$ in this specific case
Note that this series is not for the hypergeometric itself, but for $h(x)$ which is $(1x)^K$ times the hypergeometric. 
Mar 27 
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How to prove that $(1x)^b$ $_2F_1(a,b;c;x)$ can be approximated to $1\alpha x$ (with $\alpha \approx 1$) for $x\ll 1$ in this specific case
I'm pretty sure these formulas, which were obtained with the help of Maple, do involve the correct use of Pochhammer symbols. 
Mar 26 
revised 
How to prove that $(1x)^b$ $_2F_1(a,b;c;x)$ can be approximated to $1\alpha x$ (with $\alpha \approx 1$) for $x\ll 1$ in this specific case
added 530 characters in body 
Mar 26 
revised 
How to prove that $(1x)^b$ $_2F_1(a,b;c;x)$ can be approximated to $1\alpha x$ (with $\alpha \approx 1$) for $x\ll 1$ in this specific case
added 530 characters in body 
Mar 26 
revised 
How to prove that $(1x)^b$ $_2F_1(a,b;c;x)$ can be approximated to $1\alpha x$ (with $\alpha \approx 1$) for $x\ll 1$ in this specific case
added 201 characters in body 
Mar 26 
answered  How to prove that $(1x)^b$ $_2F_1(a,b;c;x)$ can be approximated to $1\alpha x$ (with $\alpha \approx 1$) for $x\ll 1$ in this specific case 
Mar 24 
revised 
Certain inverse problem related to moments
added 790 characters in body 
Mar 24 
answered  Certain inverse problem related to moments 
Mar 24 
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Is there any simpler form of this function
$F(2n+1) = c_n + d_n \sqrt{2}$ where $$c_{{m}}={\frac { \left( 4\,{m}^{2}+4\,m \right) c_{{m2}} \left( 6 \,{m}^{2}5\,m+1 \right) c_{{m1}}}{2\,{m}^{2}+m}} $$ and $$d_n = \dfrac{n!(n+1)!}{(2n+1)!} 2^{3n+1}$$ 
Mar 24 
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Is there any simpler form of this function
It appears that $F(2n) = a_n + b_n \pi$ where $$a_n ={\frac { \left( 2\,{n}^{2}+7\,n6 \right) a _{ n3}  \left( 9\,{n}^{2}14\,n+7 \right) a _{ n2 }  \left( 10\,{n}^{2}+10\,n \right) a_{ n1} }{3 \,{n}^{2}3\,n}} $$ while $$b_n = \dfrac{(2n+1)!}{(n!)^2 2^{n+2}}$$ 
Mar 20 
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quadratic matrix equation
(Correction of earlier comment) If $D$ is nonsingular, $\det(X) = \pm i$ in odd dimension, $\pm 1$ in even dimension. 
Mar 20 
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quadratic matrix equation
How do you know $X$ is diagonalizable? 