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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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