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   sci.math.symbolic      Symbolic algebra discussion      10,432 messages   

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   Message 8,435 of 10,432   
   Axel Vogt to All   
   Int(exp*BesselI0(sqrt)): Gradshteyn & Ry   
   04 Oct 13 22:25:19   
   
   From: &noreply@axelvogt.de   
      
   The book says: Int( exp(-x*a) * BesselI(0, b*sqrt(-x^2+1)), x = -1 .. 1) =   
   = 2*sinh(a^2+b^2)/sqrt(a^2+b^2)   
      
   For a=0 I obtain that it is 2*sinh(b)/b, using Maple (sketch: write Bessel   
   as series and integrate termwise; evaluating the infinite series gives it).   
   Numerical tests do confirm that.   
      
   Is somebody aware of the root of the proof in G&R (can not find an erratum,   
   but some usage of the formula) to eliminate the possible typo?   
      
   --- SoupGate-Win32 v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)   

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