[Date Index]
[Thread Index]
[Author Index]
Re: troublesome integral
*To*: mathgroup at smc.vnet.net
*Subject*: [mg126011] Re: troublesome integral
*From*: "Stephen Luttrell" <steve at _removemefirst_stephenluttrell.com>
*Date*: Fri, 13 Apr 2012 04:44:42 -0400 (EDT)
*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com
*References*: <jm64ib$6la$1@smc.vnet.net>
You can rewrite the integral as
Integrate[
Cos[\[Alpha] + \[Beta]] Exp[I z Cos[\[Beta]]], {\[Beta], 0, 2 \[Pi]},
Assumptions -> z \[Element] Reals]
which can be rearranged as (the Sin[\[Alpha]] Sin[\[Beta]] part integrates
to zero)
Integrate[
Cos[\[Alpha]] Cos[\[Beta]] Exp[I z Cos[\[Beta]]], {\[Beta], 0,
2 \[Pi]}, Assumptions -> z \[Element] Reals]
which evaluates to
2 I \[Pi] BesselJ[1, z] Cos[\[Alpha]]
Over the years I too have encountered this problem with evaluating integral
representations of Bessel functions, and the only solution I have found is
to give mathematica a helping hand, as above.
--
Stephen Luttrell
West Malvern, UK
"peter lindsay" <pl0 at me.com> wrote in message
news:jm64ib$6la$1 at smc.vnet.net...
>
> A couple of colleagues wondered about this. I've sent it on to support @
> wolfram who are escalating it to the developers. Possibly someone here has
> an answer though ?
>
> Integrate[Cos[\[Beta]] Exp[I z Cos[\[Beta]-\[Alpha]]],{\[Beta],0,2
> \[Pi]},Assumptions->z\[Element]Reals]
>
> doesn't seem to run.
>
> Answer should be
>
> 2 I \[Pi] BesselJ[1,z] Cos[\[Alpha]] [ I think ]
>
> thanks
>
>
> Peter Lindsay
>
>
Prev by Date:
**Re: Replace a vertical line in ListPlot**
Next by Date:
**Re: What characters are allowed in mathematica variable names? i.e. how**
Previous by thread:
**Re: troublesome integral**
Next by thread:
**Re: troublesome integral**
| |