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Student Support Forum: 'Bessel integral - Strange Hypergeometric Function' topicStudent Support Forum > General > "Bessel integral - Strange Hypergeometric Function"

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Hugo
11/26/12 12:02pm

Dear all,
I need to evaluate analytically the integral of a Bessel function J_0(k*r) times an simple rational function 1/(k-k0) (k is the integration variable and k0 a constant) and Mathematica does the job pretty well with a little help.

The point is that I get a function that is very unclear in the output. Indeed, in addition to a J_0 function and a Struve function H_0, I get a:
"Hypergeometric0F1Regularized^(1,0)(1,-(1/4)k0^2 r^2)"
which could be very nice if there wasn't this "(1,0)" exponent. Since it would give nothing but another J_0 function.

Usually such exponent refers of course to the derivatives of the function but here it cannot be since: first there is only one variable "r" and second, I checked plotting the derivative together with this function that they are very different. Furthermore the derivative of "Hypergeometric0F1Regularized" is known by Mathematica so it should be explicitely given in that case. Very strange...

I really need to figure out what it is to have a usable analytical solution. I attach the nb file for clarity.

I thank you all in advance, cheers !

Attachment: Forum.nb, URL: ,

Subject (listing for 'Bessel integral - Strange Hypergeometric Function')
Author Date Posted
Bessel integral - Strange Hypergeometric Function Hugo 11/26/12 12:02pm
Re: Bessel integral - Strange Hypergeometric Fu... yehuda 11/28/12 01:36am
Re: Re: Bessel integral - Strange Hypergeometri... Hugo 11/28/12 2:13pm
Re: Re: Re: Bessel integral - Strange Hypergeom... Michael 12/01/12 11:09pm
Re: Re: Re: Re: Bessel integral - Strange Hyper... Hugo 12/04/12 03:08am
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