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Thread: leading coefficient

  1. #1
    Super Member
    Aug 2009

    leading coefficient

    given that { f(x), f' (x)..., f^n (x)} is a basis for Pn,

    then a_0 f(x)+ a_1 f'(x)+...a_n f^n (x)=0 , hw can you tell that the leading coefficient is a_0 a_n and that

    for a_1 f'(x)+...a_n f^n (x)=0 where a_0 f(x)=0 then the leading coefficient is 2a_1 a_n?
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  2. #2
    Nov 2010
    I'm not sure what you mean by leading coefficient; leading coefficient of what?

    Since the set $\displaystyle \left\{ f,f^\prime ,\ldots ,f^{(n)}\right\}$ is a basis for $\displaystyle \mathbb{P}_n$, the first equation you have implies each $\displaystyle a_i$ is 0.
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