Sequence of number

  • #1
391
0

Main Question or Discussion Point

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.
 

Answers and Replies

  • #2
HallsofIvy
Science Advisor
Homework Helper
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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.
 
  • #3
391
0
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.
 
  • #4
607
0
I don't think your integral should start at n=0 should it? Maybe x=0 ...
 

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