# Gottfried Helms

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bio website go.helms-net.de location Germany age 61 member for 3 years, 9 months seen 4 hours ago profile views 1,058
Mathematics is only a hobby - although I have done undergrad courses in the 70ties. But part of my job was doing statistics and this kept me near my favourite subject "linear algebra" (programmed factor-analysis and a matrix-orientated calculator MatMate). Around 2002 I came in contact with the internet-community in math-newsgroups and could improve my Collatz-discussion. Next subject was the Bernoulli-numbers, then integer matrices and since 2006 the problem of iterated exponentiation aka tetration. Serving half-term jobs in teaching here at the university I found time to fiddle with that subjects in depth - and found love with the exploratory approach and impulse of the 18'th century numbertheory, namely L.Euler, "the master of us all"... Due to lack of formal education I've to do my "research" widely on my own - but that's what I just like: to find structure, pattern, laws from the ground.

 10 Is $\sum\limits_{n=0}^\infty x^n / \sqrt{n!}$ positive? 8 The functional equation $f(f(x))=x+f(x)^2$ 7 Eigenvalues of infinite matrices 7 German mathematical terms like “Nullstellensatz” 4 Is $\sum\limits_{n=0}^\infty x^n / \sqrt{n!}$ positive?

# 1,650 Reputation

 +20 How this expression leads to the given sequence +5 Is that series-transformation known in the context of divergent summation? +20 Infinite matrix leading eigenvector problem +10 Euler's divergent series sum n!*(-1)^n: what is known about the resulting constant?

# 17 Questions

 7 Trouble with Jordan form of the truncated Carleman-matrix for $\sin(x)$ as size $n$ goes to infinity 6 Fermat-quotient of “order” 3: I found $68^{112} \equiv 1 \pmod {113^3}$ - are there bigger examples known? 6 Efficient (divergent) summation for sum of zetas at negative arguments? 4 Is that series-transformation known in the context of divergent summation? 4 Can the relative count of the primefactors in $\small \lim_{w\to\infty}\prod_{k=1}^w (p_k-1)$ be determined analytically?

# 70 Tags

 27 reference-request × 14 20 functional-equations × 7 26 ds.dynamical-systems × 7 17 generating-functions × 4 25 ca.analysis-and-odes × 8 13 fractional-iteration × 5 23 sequences-and-series × 12 12 co.combinatorics × 7 21 nt.number-theory × 21 9 collatz-conjecture × 3

# 15 Accounts

 Mathematics 11,827 rep 11351 MathOverflow 1,650 rep 1414 Cross Validated 395 rep 37 German Language 283 rep 28 Area 51 151 rep 14