From: &noreply@axelvogt.de   
      
   On 05.10.2013 15:07, G. A. Edgar wrote:   
   > In article <524FF9CF.6F7CD843@freenet.de>,    
   > wrote:   
   >   
   >> Axel Vogt schrieb:   
   >>>   
   >>> 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)   
   >>>   
   ...   
   >> There is no entry 6.616.5 for   
   >>   
   >>   INT(exp(-x*a)*BesselI(0, b*sqrt(1-x^2)), x, -1, 1)   
   >>   
   >> in my 1981 edition of Gradshteyn & Ryzhik; it must have been added   
   >> later. I suggest to try the modified evaluation   
   >>   
   >>   2*sinh(sqrt(a^2+b^2))/sqrt(a^2+b^2)   
   >>   
   >> which holds at b=0 as well as a=0, since BesselI(0, 0) = 1. It is also   
   >> in full agreement with a numerical evaluation of the integral on Derive   
   >> giving 2.199018052 for a = 0.3 and b = 0.7. Doing the general integral   
   >> symbolically may be difficult; related integrals under 6.616 in my   
   >> edition are all taken from Magnus and Oberhettinger, 1948.   
   ...   
   >> Martin.   
   >   
   > In my 1980 copy of G&R (English translation of the fourth Russian   
   > edition), there is such an entry, with note 3 meaning "added in the   
   > third edition".  However (as Axel suggests) the value is   
   > 2*sinh(sqrt(a^2+b^2))/sqrt(a^2+b^2)   
      
   Sorry, I have to beg for pardon: it is *my* fault and *no* typo,   
   I had it false in my worksheet, Mist!   
      
   It is stated as G. A. Edgar says.   
      
   PS:   
   Mine is edition 6 from 2000, the formula is on page 690 (and a   
   related one in 6.625.11, p. 696, by partial integration wrt I0).   
   At least now I know that "MO" in the right margins may mean the   
   book of Magnus & Oberhettinger   
      
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