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

### NY Lost Funds

 euclidean I agree TRWBW euclidean: so you want do do something like f(x)-x*f(x)=f(x)/x?oops euclidean TRWBW: 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 TRWBW wait, let me get that straight euclidean TRWBW: then you multiply this equation by x^n TRWBW so x^2*f=x*f+x euclidean nobefore that :) TRWBW ?why not just jump there euclidean 1/x^2 F_{n+2} x^{n+2} = 1/x F_{n+1} x^{n+2} + F_n x^n TRWBW yeah right, that's what i meant euclidean now you sum up for n = 0,+oobut this implies convergence of the initial power series TRWBW euclidean: 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 TRWBW if 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) euclidean hmm.. 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 TRWBW and if f(0)=f'(0)=1, then those a_n must be the fibonocci numbers clarity_ i'm about 90% sure it's cool euclidean TRWBW: I definitely agreeTRWBW: so I should start with this function that fell from the sky, prove its convergence and then extract the terms in the sequence TRWBW euclidean: nothing wrong with that. it's rigorous. euclidean TRWBW: the other way around is not that rigurous right? I mean supposing that the series is convergent, and then prove it in the end TRWBW euclidean: nope. euclidean TRWBW: 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 TRWBW euclidean:maybe said that wrong, you can't assume it's convergent in proving its convergent, but that's obviouseuclidean: 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. euclidean TRWBW: right.. :) false implies anythingTRWBW: thanks for a help TRWBW np 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 HiLander re the earlier discussion on generating functions and convergenceconvergence is irrelevant, power series manipulations are done over the ring of formal power series euclidean HiLander: I agree.. but that's when working with generating functions, algebraically HiLander no euclidean HiLander: I was rather solving the problem using power series of a real variable