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Integration of an infinite product

  1. Apr 5, 2013 #1
    Hey guys, what sup
    I need you all to help me in resolving the integral of an infinite product...
    i was thinking of perhaps integrating by parts, but when yo do that the integration becomes brutally expansive...
    any ideas?
    thank you all very much

    the variable which is aimed to be integrated is x btw...
     

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  3. Apr 5, 2013 #2

    pwsnafu

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    You wrote down a finite product. Do you in fact want ##\int \prod_{m=1}^\infty (x^2 + m) \, dx##?
     
  4. Apr 6, 2013 #3
    for example

    (x*x+1)*(x*x+2)*(x*x+3)*(x*x+4) = x^8 + a*x^6 + b*x^4 + c*x^2 + 1*2*3*4

    1*2*3*4 = 4!


    (x*x+1)*(x*x+2)*(x*x+3)*(x*x+4) = x^8 + 10x^6 + 35x^4 + 50x^2 + 24

    Each member must be integrated.

    ∫ x^8 + 10x^6 + 35x^4 + 50x^2 + 24 dx =

    = x^9/9 + 10x^7/7 + 7x^5 +50x^3/3 +24x + C

    kamke
     
  5. Apr 6, 2013 #4

    mfb

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    The problem is to get a general formula for those coefficients.

    Basically ##\displaystyle \sum_{i,j,...=1, i<j<...}^n i*j*k*...## with 0 to n indices in the sum.
    The second sum, for example, sums 1*2+1*3*...+1*n + 2*3+2*4+...+2*n+...
     
  6. May 23, 2013 #5
    MFB, that answer seems a bit unclear
    perhaps any other ideas?
     
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