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Angelo Melino

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8 years, 275 days
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These are questions asked by Angelo Melino

Is there an error in Maple's BesselI(v,z...

Angelo Melino 45 Maple 2019
integral bessel
December 13 2019
1 1

I compared the numerical value of an integral expression in Gradshteyn and Rhyzhik (8.431.5) for the BesselI(v,z) function to the BesselI(v,z) function in Maple 2019.2 and got different answers.  The GR expression is the difference of two integrals and it looks like Maple only evaluates the first integral, which is correct only if the order v is an integer.  Please see the attached.

BesselI.mw

Why can't Maple evaluate this integral n...

Angelo Melino 45 Maple 2019
integration numeric
November 06 2019
1 4


I'm trying to evaluate an integral, but after several hours, MAPLE 2019 is unable to return an answer.  My CPU and memory are not being taxed, and the integrand appears well behaved.  Please see below. Any advice?

restart

istar := y*sinh(Pi*y)*exp(-alpha*y^2)*LegendreP(-1/2+I*y, 1+u)

y*sinh(Pi*y)*exp(-alpha*y^2)*LegendreP(-1/2+I*y, 1+u)

 (1)

Istar := `assuming`([int(istar, y = 0 .. infinity)], [alpha > 0, u > 0])

int(y*sinh(Pi*y)*exp(-alpha*y^2)*LegendreP(-1/2+I*y, 1+u), y = 0 .. infinity)

 (2)

alpha := 1; u := 2

2

 (3)

plot(istar, y = 0 .. 40)

  

evalf(Istar)

``


 

Download Istar.mw

 

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