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Hadamard Product for Riemann's Xi Function

  1. Dec 2, 2009 #1
    What is the infinite product for the function
    [tex]\Xi(s)=\Gamma\left(\frac{s}{2}\right)\pi^{-s/2}\zeta(s)[/tex]
    ?
     
  2. jcsd
  3. Dec 9, 2009 #2
    You can manipulate the Hadamard's zeta function infinite product to get your answer.
     
  4. Dec 21, 2009 #3

    Avodyne

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    Science Advisor

    [tex]{\prod_n (1-s/s_n)\over s(s-1)}[/tex]

    where [itex]s_n[/itex] is a complex zero of [itex]\zeta(s)[/itex].
     
  5. Feb 17, 2010 #4
    Thank you Avodyne
     
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