Timeline for From power series to differential equations
Current License: CC BY-SA 2.5
5 events
| when toggle format | what | by | license | comment | |
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| Dec 27, 2010 at 2:40 | comment | added | Gerry Myerson | @Mariano, so, if the question had been whether for any real number $\alpha$ we can find, or prove there exists, a linear polynomial that characterizes it, you would say, yes, $x-\alpha$, and I would say that's cheating, because you generally can't write $\alpha$. I take your point; but I suspect OP had in mind an equation that didn't make such blatant use of the given power series, but rather used only, say, rational numbers and common functions. So I think it's up to OP to clarify intent. | |
| Dec 26, 2010 at 16:05 | comment | added | Mariano Suárez-Álvarez | The question asks "can we find, or prove that it exists"... | |
| Dec 26, 2010 at 16:00 | comment | added | Gerry Myerson | @Mariano, yes, but: if you propose to write the right side out as an infinite power series, then you can't actually write it down, while if you just call the right side $f$, then eventually you run out of names for power series, without running out of power series. | |
| Dec 26, 2010 at 15:44 | comment | added | Mariano Suárez-Álvarez | @Gerry: not really: for every (formal!) power series $f$ there is an ODE $u'(x)=f(x)$, so there are at least as many ODEs as series. | |
| Dec 26, 2010 at 15:39 | history | answered | Gerry Myerson | CC BY-SA 2.5 |