Timeline for Closed-form for modified formal power series
Current License: CC BY-SA 4.0
12 events
| when toggle format | what | by | license | comment | |
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| S Mar 15, 2019 at 21:10 | history | suggested | Glorfindel | CC BY-SA 4.0 |
broken image fixed (click 'rendered output' or 'side-by-side' to see the difference); for more info, see https://meta.mathoverflow.net/a/4058/70594
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| Mar 15, 2019 at 20:40 | review | Suggested edits | |||
| S Mar 15, 2019 at 21:10 | |||||
| Jul 27, 2011 at 22:43 | comment | added | StevenJ | Got it. Do you think it might help figure out f(x)? | |
| Jul 26, 2011 at 16:27 | comment | added | Gottfried Helms | @STevenj: but to construct the Carlemanmatrix is easy! Just assume exponent p=0 in the above table and compute the coefficients - these are just the coefficients of the column c=0 of the Carleman-matrix (actually it is everywhere zero except at x^0). Then use p=1 - the new coefficients are that of column c=1; use p=2 in the above table compute the coefficients at each x and have the coefficients of column c=2 of the Carleman-matrix. And so on. No recursion needed... | |
| Jul 26, 2011 at 14:02 | comment | added | StevenJ | Thanks for taking the time to make the table! Certainly using a computer I can calculate the coefficients of $P_T$ or $P^n$ to any order. The key difficulty is to calculate the coefficients analytically so that I can determine if f(x) has a closed-form solution. Carleman matrices are new to me but seem to do the job pretty well. Do you think it it possible to calculate the Carleman matrix for P(C) in a simple way? From my experiments the off-diagonal terms have a fairly complicated structure which doesn't obviously allow you to write down the whole matrix if you know the coefficients $a_n$. | |
| Jul 26, 2011 at 10:19 | history | edited | Gottfried Helms | CC BY-SA 3.0 |
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| Jul 26, 2011 at 10:10 | history | edited | Gottfried Helms | CC BY-SA 3.0 |
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| Jul 26, 2011 at 9:44 | history | edited | Gottfried Helms | CC BY-SA 3.0 |
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| Jul 26, 2011 at 9:38 | history | edited | Gottfried Helms | CC BY-SA 3.0 |
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| Jul 26, 2011 at 9:33 | history | edited | Gottfried Helms | CC BY-SA 3.0 |
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| Jul 25, 2011 at 21:48 | comment | added | StevenJ | Thanks a lot for responding. Unfortunately $P^n$ does refer to power, not iteration. I've edited the question to make that clearer as well as to explicitly write the $b_n$ coefficients and the start of $P_T(C)$ and f(x). Although I'm interested to see what you were able to construct. What is the matrix-operator M for the function P(x)? | |
| Jul 25, 2011 at 20:56 | history | answered | Gottfried Helms | CC BY-SA 3.0 |