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Feb
3
comment Asymptotic behavior of a function
... and when $n$ is odd you don't even need hypergeometric functions (it is a simple integration by parts exercise). For $n = 3$ it is proportional to $\sin(t)/t$. For $n = 5$ to $\cos(t)/t + \sin(t)/t^2$ or something like that.
Feb
3
comment Asymptotic behavior of a function
What is $\omega_1$? (In particular, what values does it take? When $n = 2$ is $\omega_1 \in [-1,1]$ or is it in $[0,2\pi)$?)
Feb
2
reviewed Leave Closed Is the 3x+1 problem solved?
Feb
2
reviewed Looks OK How to compute $\int_0^{\frac{\pi}{2}} \frac{\ln(\sin(x))}{\cot(x)}\ \text{d}x$
Feb
2
reviewed Looks OK Find the equation of a non-linear relation given 2 points
Feb
2
awarded  Good Question
Jan
15
comment Convolution of delta-ish functions
Note however that $\delta(x)/x$ can be interpreted as a well-defined linear functional on smooth functions vanishing at the origin. The pairing $\langle \delta(x)/x,f(x)\rangle$ for such functions can be interpreted to equal $f'(0)$. However in this interpretation, since the test function space is not translation invariant, you cannot define meaningfully the convolution.
Jan
15
comment Convolution of delta-ish functions
Not as a distribution. You may try to interpret $1/x$ as the principal value distribution; but then its singular support is precisely the origin, and thus coincide with that of the Dirac delta. This means we cannot expect a meaningful "product". Alternatively, were the product well defined, we would expect that its Fourier transform to equal that of the convolution of the two Fourier transforms. $\hat{\delta} = 1$ while $\hat{p.v. 1/x} = H(x)$. Neither have compact support and so again their "convolution" is not well-defined.
Jan
8
awarded  Enlightened
Jan
7
awarded  Nice Answer
Jan
5
awarded  Nice Answer
Jan
3
awarded  Notable Question
Dec
21
reviewed Close Continuum hypothesis outside of ZFC
Dec
21
reviewed Close Compare a non-computable real number to a rational
Dec
21
reviewed Leave Open Need help with $\int_0^\infty\frac{e^{-x}}{\sqrt[3]2+\cos x}dx$
Dec
21
reviewed Close Prove that $\sqrt{2} + \sqrt[3]{3}$ is irrational
Dec
21
reviewed Leave Open Prove ${2}^{n}\cdot(2m+1)-1 $ is invertible
Dec
20
comment Prove that every polynomial from a finite Banach space to another Banach space has an unique representation in terms of coordinate functionals
I would suggest (1) first find a basis of $E^m$ in terms of copies of $e_i$. (2) find a dual basis in terms of $\xi_i$. (3) Since $E^m$ is finite dimensional, find the matrix of $A$ in terms of the dual basis of $E^m$. (4) Re-interpret that using your formula for $P$ in terms of $A$.
Dec
20
comment Prove that every polynomial from a finite Banach space to another Banach space has an unique representation in terms of coordinate functionals
It may help to include the definition (in your context) of what it means to be a polynomial. For example, I would have taken the finite sum formula to be a definition to start with.
Dec
19
awarded  Great Question