#math - Sun 1 Apr 2007 between 04:45 and 05:23

NY Lost Funds



euclideanI agree
TRWBWeuclidean: so you want do do something like f(x)-x*f(x)=f(x)/x?
oops
euclideanTRWBW: so consider f(x) = Sum[F_n x^n, n = 0, +oo]. You know that F_n satisfies F_{n+2} = F_{n+1} + F_n
TRWBWwait, let me get that straight
euclideanTRWBW: then you multiply this equation by x^n
TRWBWso x^2*f=x*f+x
euclideanno
before that :)
TRWBW?
why not just jump there
euclidean1/x^2 F_{n+2} x^{n+2} = 1/x F_{n+1} x^{n+2} + F_n x^n
TRWBWyeah right, that's what i meant
euclideannow you sum up for n = 0,+oo
but this implies convergence of the initial power series
TRWBWeuclidean: if you do it and you get some f and it has a power series that converges and it satisfies the equation, then that power series must satisfy your condition. it doesn't matter if you cheated a bit to get the f
clarity_http://rafb.net/p/pNH10N77.html
TRWBWif f=x*f+x^2*f, and f has a power series that converges, then the terms for f must satisfy a_n=a_(n-1)+a_(n-2)
euclideanhmm.. so it's not ok if I suppose that the series is convergent from the start, and then prove it in the end?
clarity_hmm, does that look kosher
TRWBWand if f(0)=f'(0)=1, then those a_n must be the fibonocci numbers
clarity_i'm about 90% sure it's cool
euclideanTRWBW: I definitely agree
TRWBW: so I should start with this function that fell from the sky, prove its convergence and then extract the terms in the sequence
TRWBWeuclidean: nothing wrong with that. it's rigorous.
euclideanTRWBW: the other way around is not that rigurous right? I mean supposing that the series is convergent, and then prove it in the end
TRWBWeuclidean: nope.
euclideanTRWBW: I agree.. so the other option would only be generating functions, is that rigurous?
TRWBW: but I assume I cannot use the Maclaurin formula in a generating functions context
TRWBWeuclidean:maybe said that wrong, you can't assume it's convergent in proving its convergent, but that's obvious
euclidean: i think you know everything i do at this point, don't know what more to say. time for me to turn into a pumpkin.
euclideanTRWBW: right.. :) false implies anything
TRWBW: thanks for a help
TRWBWnp
clarity_it's is kinda funny... i'm watching this thing in a language that i don't understand that's being translated into another language i don't understand
HiLanderre the earlier discussion on generating functions and convergence
convergence is irrelevant, power series manipulations are done over the ring of formal power series
euclideanHiLander: I agree.. but that's when working with generating functions, algebraically
HiLanderno
euclideanHiLander: I was rather solving the problem using power series of a real variable

Page: 4 11 18 25 32 39 46 53 

IrcArchive

NY Lost Funds