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 | no before 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,+oo but 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 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 |

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 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. |

euclidean | TRWBW: right.. :) false implies anything TRWBW: 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 convergence convergence 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 |