Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    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

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

    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

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

    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 ...
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Sequence of number
  1. Number Sequence (Replies: 2)

Loading...