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1d
comment Integration of a polylogarithm: Is this function known?
Is this an error? I've never seen two times $dx$ in one integration formula
2d
comment Prove that $24^{31}$ is congruent to $23^{32}$ mod 19.
To do your last formula mentally it seems more practical to reorder: $(5 \cdot 4) \cdot (6 \cdot -3) \cdot (-2) \equiv (1) \cdot (1) \cdot (-2) \equiv -2 \pmod {19} $
Apr
29
comment There exists an irrational number z such that x<z<y
Consider to work with the different part in the infinite or finite decimal-digit-representations of x and y and to construct a number between them based on the first different digit...
Apr
29
accepted Where does the iteration of the exponential map switch from one fixpoint to the 3-periodic fixpoint cycle?
Apr
28
revised Convergence properties of $z^{z^{z^{…}}}$ and is it “chaotic”
added 223 characters in body
Apr
28
answered Convergence properties of $z^{z^{z^{…}}}$ and is it “chaotic”
Apr
27
comment Convergence properties of $z^{z^{z^{…}}}$ and is it “chaotic”
The Tetaration-forum database has references to 5 Baker/Rippon articles into the "zentralblatt", for instance this one: zbmath.org/?q=an:0644.30014 Perhaps from there you can proceed. The link in the Tetration-databse was eretrandre.org/rb/…. But I don't know whether this is openly available.
Apr
26
answered Is this a proof for the Collatz conjecture
Apr
26
comment How many steps to reach 1? (Collatz Conjecture)
Using Pari/GP the following results occur in less than a second: . . . . . . . . . . . . . . $\small {m=3456;w=10^{m-2};\\ n1=260 *w; [n,it] = [1, 58968]\\ n1=261 *w; [n,it] = [1, 62437]\\ n1=262 *w; [n,it] = [1, 61739]\\ n1=263 *w; [n,it] = [1, 61907]\\ n1=264 *w; [n,it] = [1, 59516]\\ n1=265 *w; [n,it] = [1, 61266]\\ n1=266 *w; [n,it] = [1, 60325]\\ n1=267 *w; [n,it] = [1, 60837]\\ n1=268 *w; [n,it] = [1, 61310]\\ n1=269 *w; [n,it] = [1, 61491]\\ } $ . . . . . . . .
Apr
25
comment Regularizing the sum of all factorials
Is it sure, that Borel-summation can be applied here? I was convinced, that to be Borel-summable a series must have alternating signs (if I understood Konrad Knopp's book correctly)
Apr
25
comment Good problems to do while reading Hardy's book on divergent series?
Konrad Knopp in his book on series has a chapter about divergent series (chap 13 in the german edition) and has many exercises. (Don't have the exact english title at hand, but the book has been at least partially readable via google-books some years ago)
Apr
25
comment How many steps to reach 1? (Collatz Conjecture)
For numbers of certain structures the number of iterations can be directly determined, so for numbers of the form $n=2^m$. For numbers of the form $ n= a \cdot 2^m$ one can at least find the number of iterations down to $n' = a$ similarly. Btw., your number needs 59516 iterations to reach n'=1 ...
Apr
25
revised Existence of an $n\times n$ real matrix $A$ such that $A^2=-I$.
added 159 characters in body
Apr
25
revised Existence of an $n\times n$ real matrix $A$ such that $A^2=-I$.
added 128 characters in body
Apr
25
revised Existence of an $n\times n$ real matrix $A$ such that $A^2=-I$.
added 96 characters in body
Apr
25
answered Existence of an $n\times n$ real matrix $A$ such that $A^2=-I$.
Apr
25
comment Existence of an $n\times n$ real matrix $A$ such that $A^2=-I$.
$A^4=I$ then $A^3 = A^{-1}$ (but I don't know whether this helps...)
Apr
25
revised Relation between Cholesky and SVD
typo - the name of the inventor of the method was "Cholesky"
Apr
25
comment Relation between Cholesky and SVD
If you can handle squareroots of negative numbers ($\to$ complex numbers) there's no problem with non-positive definite matrices.
Apr
25
revised I have a answer to a question about trace. Is there an easier answer to this question?
typo in subject, typos in text