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## #101 2016-11-05 08:16:00

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

### Re: Sum of an integral involving Bessel functions

That could account for some of the differences.

I can plot that integrand but I do not understand the plot that I can see.

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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## #102 2016-11-05 08:17:42

zetafunc
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Registered: 2014-05-21
Posts: 2,109
Website

### Re: Sum of an integral involving Bessel functions

What do you see?

I've tried plotting stuff and I get an empty graph.

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## #103 2016-11-05 08:27:24

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

### Re: Sum of an integral involving Bessel functions

Hold on I will upload some images.

Might be easier to give the commands.

RegionPlot[((x^2 + y^2)^(-1/2)) (((100 - x)^2 + (100 - y)^2)^(-1/2))*
BesselJ[1, (x^2 + y^2)^(1/2)]*BesselJ[1, (((100 - x)^2 + (100 - y)^2)^(1/2))] > 0, {x, -10, 10}, {y, -10, 10}]
RegionPlot[((x^2 + y^2)^(-1/2)) (((100 - x)^2 + (100 - y)^2)^(-1/2))*
BesselJ[1, (x^2 + y^2)^(1/2)]*BesselJ[1, (((100 - x)^2 + (100 - y)^2)^(1/2))] < 0, {x, -10, 10}, {y, -10, 10}]

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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## #104 2016-11-05 08:44:21

zetafunc
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Registered: 2014-05-21
Posts: 2,109
Website

### Re: Sum of an integral involving Bessel functions

Thanks for the code. Those plots seem weird, but form an intriguing pattern.

Last edited by zetafunc (2016-11-05 09:47:02)

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## #105 2016-11-05 09:15:00

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

### Re: Sum of an integral involving Bessel functions

I have no idea what that means except it seems to indicate that integrand is sometimes positive and sometimes not.

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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## #106 2016-11-06 07:30:34

zetafunc
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Registered: 2014-05-21
Posts: 2,109
Website

### Re: Sum of an integral involving Bessel functions

No responses yet on MO. Might be worth asking the same question on MathSE.

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## #107 2016-11-06 11:38:34

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

### Re: Sum of an integral involving Bessel functions

I do not know how the entire world feels about that but I generally avoid doing that.

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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## #108 2016-11-06 21:02:39

zetafunc
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Registered: 2014-05-21
Posts: 2,109
Website

### Re: Sum of an integral involving Bessel functions

It is either that or set up a bounty. (Or just solve it myself, of course.)

Last edited by zetafunc (2016-11-07 01:16:57)

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## #109 2016-11-07 05:22:00

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

### Re: Sum of an integral involving Bessel functions

Hi;

Bounties do not really make anyone smarter than they were before. Still, that is a possibility. How much will you offer?

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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## #110 2016-11-08 01:17:54

zetafunc
Moderator
Registered: 2014-05-21
Posts: 2,109
Website

### Re: Sum of an integral involving Bessel functions

I'd offer the minimum if I were offering a bounty. But it might also be worth contacting my supervisor -- I haven't heard from him yet though (I sent him my proof on Thursday, but he's currently away so will probably not be able to get back to me for a while).

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## #111 2016-11-08 03:21:44

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

### Re: Sum of an integral involving Bessel functions

What place will you post the bounty?

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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## #112 2016-11-08 03:23:57

zetafunc
Moderator
Registered: 2014-05-21
Posts: 2,109
Website

### Re: Sum of an integral involving Bessel functions

Maybe MathSE, because there are more people on there and I have 318 rep to spare there. On MO I only have 116.

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## #113 2016-11-08 03:33:05

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

### Re: Sum of an integral involving Bessel functions

There are pros and cons. The people on the MathSE that could answer already have gazillions of rep points. A bounty may not interest them. The ones that might answer attracted by the bounty are more unknown.

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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