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Sequence of number

  1. Mar 13, 2010 #1
    given the sequence (power series) [tex] g(x)= \sum_{n\ge 0}a(n)(-1)^{n}x^{n} [/tex]

    if i define [tex] a(n)=\int_{n=0}^{\infty}dxf(x)x^{n} [/tex] (1)

    if [tex] f(x)>0 [/tex] on the whole interval [tex] (0,\infty) [/tex] , is the solution to (1) unique ?? , this means that the moment problem for a(n) would have only a solution.
  2. jcsd
  3. Mar 14, 2010 #2


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    How can we tell you if "the solution to (1)" is unique when there is nothing labeled (1)?

    And what does an integral of f(x) have to do with a sum of g(x)?

    Frankly, nothing here makes any sense.
  4. Mar 14, 2010 #3
    i meant

    is the solution to


    where a(n) is given but f(x) is unknown UNIQUE is f(x) is positive on the whole interval (0,oo) ??? , i mean if the integral equation


    has ONLY a solution provided f(x) is always positive, thanks.
  5. Mar 14, 2010 #4
    I don't think your integral should start at n=0 should it? Maybe x=0 ...
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