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Topic: Int(exp*BesselI0(sqrt)): Gradshteyn & Ryshik, 6.616.5 ?
Replies: 5   Last Post: Oct 6, 2013 12:42 PM

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Axel Vogt

Posts: 1,036
Registered: 5/5/07
Int(exp*BesselI0(sqrt)): Gradshteyn & Ryshik, 6.616.5 ?
Posted: Oct 4, 2013 4:25 PM
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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?



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