Gottfried Helms
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Registered User
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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.
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1d |
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Even more generalized Catalan numbers The wikipedia is clickable in this notation: en.wikipedia.org/wiki/… |
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May 7 |
awarded | ● Nice Answer |
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May 4 |
revised |
What is the (fractional) half-derivative of zeta at $s=0$ (and how to compute it)? edited tags |
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May 4 |
revised |
What is the (fractional) half-derivative of zeta at $s=0$ (and how to compute it)? added 2 characters in body; added 3 characters in body; edited body |
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May 4 |
asked | What is the (fractional) half-derivative of zeta at $s=0$ (and how to compute it)? |
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Apr 20 |
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Efficient (divergent) summation for sum of zetas at negative arguments? I see; I've made a sign-error, sorry. |
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Apr 20 |
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Efficient (divergent) summation for sum of zetas at negative arguments? hmm, if I feed the last mentioned function into Pari/GP I get for $s=\epsilon$ the result of $\epsilon^{−1}$ for epsilon near zero |
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Apr 19 |
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Efficient (divergent) summation for sum of zetas at negative arguments? @i707107: no, I've no proof for the guessed algebaric identity; so far it is only the numerical allusion - however I've got it to 40 digits instead of 15 now... |
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Apr 19 |
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Efficient (divergent) summation for sum of zetas at negative arguments? added 212 characters in body |
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Apr 19 |
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Efficient (divergent) summation for sum of zetas at negative arguments? added example with Borel-summation |
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Apr 19 |
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Efficient (divergent) summation for sum of zetas at negative arguments? @joro: are you sure that are methods for divergent summation? And if, are they strong enough? For instance, using "sumalt" in Pari/GP is not strong enough although it is in general a very useful procedure for divergent summation. |
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Apr 19 |
revised |
Efficient (divergent) summation for sum of zetas at negative arguments? added 22 characters in body |
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Apr 18 |
asked | Efficient (divergent) summation for sum of zetas at negative arguments? |
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Mar 29 |
awarded | ● Citizen Patrol |
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Mar 23 |
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Efficient way for computation of derivatives of $f(x) = \zeta(1-x) + 1/x $ at integer x? @Carlo - thank you very much; I'll take a deeper look at it later... |
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Mar 9 |
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Efficient way for computation of derivatives of $f(x) = \zeta(1-x) + 1/x $ at integer x? Ah, so I see, there was possibly a misunderstanding. I have the first 500 Stieltjes constants to 1000 digits by a nice, small procedure. What I was trying to do, was to give a sense to the sum-of-all-Stieltjes numbers, by some summation-procedure. That procedure requires to use the derivatives of the zetas in a certain manner in finite sums as written above. That finite sums, having more and more terms according to the increasing parameter c, approximate something like 0.4990749...xyz , but convergence is slow and needs many of the zeta's derivatives... |
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Mar 8 |
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Efficient way for computation of derivatives of $f(x) = \zeta(1-x) + 1/x $ at integer x? Hi Fredrik, did you mean to apply the Euler-Maclaurin formula directly at the Stieltjes-numbers? |
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Mar 8 |
revised |
Efficient way for computation of derivatives of $f(x) = \zeta(1-x) + 1/x $ at integer x? added links; added 13 characters in body |
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Mar 8 |
asked | Efficient way for computation of derivatives of $f(x) = \zeta(1-x) + 1/x $ at integer x? |
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Dec 29 |
revised |
Math for a cake added 132 characters in body |
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Dec 29 |
answered | Math for a cake |
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Dec 29 |
answered | Math for a cake |
