1d

comment 
Generating a series representation for the inverse of the operator $f(f)$
Possibly the work of Eri Jabotinski on Carlemanmatrices is relevant here. Carlemanmatrices are such operators, and "halfaoperator" is just the squareroot of the matrix. I don't have all his articles but I think he was the most advanced in this. 
2d

revised 
Summating divergent series arising from the application of the EulerMaclaurin formula to power law functions with noninteger exponents
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Oct
6 
revised 
Summating divergent series arising from the application of the EulerMaclaurin formula to power law functions with noninteger exponents
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Oct
6 
revised 
Summating divergent series arising from the application of the EulerMaclaurin formula to power law functions with noninteger exponents
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Oct
6 
revised 
Summating divergent series arising from the application of the EulerMaclaurin formula to power law functions with noninteger exponents
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Oct
6 
revised 
Summating divergent series arising from the application of the EulerMaclaurin formula to power law functions with noninteger exponents
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Oct
6 
answered  Summating divergent series arising from the application of the EulerMaclaurin formula to power law functions with noninteger exponents 
Oct
3 
revised 
Is $ \sum\limits_{n=0}^\infty x^n / \sqrt{n!} $ positive?
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Oct
3 
answered  Is $ \sum\limits_{n=0}^\infty x^n / \sqrt{n!} $ positive? 
Sep
26 
comment 
Irreducibility of Faulhaberlike Polynomials over $\mathbb Q[x]$
Ah, I agree. That's also my favorite index, btw., because I look at many of this problem with the view on matrices. However with that sum of powersproblems I let then start the seriesdefinition with $(n+1)$ to avoid powers of zero and to allow easy generalizations (of course the most simple one, series where the index is in the denominator) 
Sep
26 
comment 
Irreducibility of Faulhaberlike Polynomials over $\mathbb Q[x]$
I see the lower bound for the index $n$ in the sum being zero. Is that really meant? 
Sep
4 
comment 
Simple/efficient representation of Stirling numbers of the first kind
Ahh, thanks, that looks very promising. 
Sep
4 
comment 
Simple/efficient representation of Stirling numbers of the first kind
This looks to me like using an asymptotical inverse of the infinite Vandermondematrix $V_{r,c}=r^c$ (which of course does not exist). Like $V= S_2 \cdot \ ^dF \cdot P$ then $V \cdot P^{1} \cdot \ ^dF^{1} \cdot V = S_2 $ and then the inversion: $V^{1} \cdot \ ^dF \cdot P =S_1 $ where of course we cannot exactly use $V$ because the inversion would produce singularities. Did you get your formula by something like this? ($P$: upper triangular binomialmatrix, $S_2$ Stirling numbers 2nd kind, $ \ ^dF$ diagonalmatrix of factorials) 
Aug
25 
revised 
The factorial of 1, 2, 3, …
formatted the table 
Aug
15 
comment 
What's a natural candidate for an analytic function that interpolates the tower function?
@Daniel: in your comment seems to be an error; we have that $a^{r} = r$ instead (at least with values $1 \lt a \lt e^{1/e} $) 
Aug
10 
revised 
Convergence of expansion for fractional iteration
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Aug
10 
answered  Convergence of expansion for fractional iteration 
Jul
17 
comment 
How to prove that this equation has only one solution?
@Anthony : didn't the argument of Rhin actually mean, that the approximation of the sum of logarithms to the nearest integer is actually bad instead of good so instead of "$\le$" in your formula you needed "$\ge$" ? (I don't have access to Rhin's paper, it seems just logical to me; also I found in a paper of J. Simons/B.de Weger the argument $ (K+l) \log2  K \log3 \gt e^{13.3(0.46057+ \log K)} \qquad $ with the reference to Rhin's result. ) 
Jul
17 
awarded  Yearling 
Jun
25 
answered  How to prove that this equation has only one solution? 