       Integral with a Bessel function

• To: mathgroup at smc.vnet.net
• Subject: [mg62289] Integral with a Bessel function
• From: "Alan" <info at optioncity.REMOVETHIS.net>
• Date: Sat, 19 Nov 2005 05:54:15 -0500 (EST)
• Sender: owner-wri-mathgroup at wolfram.com

```Assume "nu" is some real number.
Mathematica (5.0) generates

Integrate[x^(2 - nu)  BesselJ[nu, x], {x,0,Infinity}] = 2^(1-nu) Sqrt[Pi] /
Gamma[nu - (1/2)],

which seems fine, but is unable to check convergence and supply a condition
on "nu".

My question:
Do you know the (least restrictive) bound on nu
for which this is valid? (and a ref. or quick proof?)

Since BesselJ(nu, x) ~ Cos(x - phase)/Sqrt(x) for large x, certainly nu >
5/2 is fine.
But the Mathematica answer suggests nu > 1/2.
However, nu = 1 seems suspiciously too large.
So the answer does not seem trivial.

Thanks!
alan

```

• Prev by Date: Re: Re: Export to PDF
• Next by Date: Re: java method in NDsolve
• Previous by thread: Re: Re: Recursion
• Next by thread: Re: Integral with a Bessel function