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#51 2011-08-13 04:02:08

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

Re: Laplace Transform of tan(t)

Okay, I will help you with specific parts if you want it but if we get egg on our face...

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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#52 2011-08-13 04:10:24

zetafunc.
Guest

Re: Laplace Transform of tan(t)

Oh boy, this doesn't look nice...

Looks like it's going to be a long night

#53 2011-08-13 04:13:46

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

Re: Laplace Transform of tan(t)

Hi;

That will yield the inverse?

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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#54 2011-08-13 04:22:25

zetafunc.
Guest

Re: Laplace Transform of tan(t)

It will at least give me the Cauchy principal value integral they are talking about,

#55 2011-08-13 04:57:47

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

Re: Laplace Transform of tan(t)

Okay, let me know what you get.

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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#56 2011-09-27 00:20:46

haron
Member
Registered: 2011-09-27
Posts: 1

Re: Laplace Transform of tan(t)

hi everybody, i have got a doubt as to if laplace transform of (cos at)/t exists. if it doesnt, please explain as to why.

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#57 2011-09-27 00:35:53

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

Re: Laplace Transform of tan(t)

Hi haron;

The transform of that does exist.

Welcome to the forum!

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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#58 2012-08-03 01:00:49

nich
Guest

Re: Laplace Transform of tan(t)

doesnt tan(t) grow faster than an exponential? then cannot use laplace?

#59 2012-08-03 02:02:31

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

Re: Laplace Transform of tan(t)

Hi nich;

Let's say that it does. Why does that mean you can not use the transform?

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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#60 2012-08-03 07:03:50

zetafunc.
Guest

Re: Laplace Transform of tan(t)

I think L{tan(at)} doesn't exist because of its discontinuities.

#61 2012-08-03 09:41:30

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

Re: Laplace Transform of tan(t)

Hi zetafunc.;

Yes, the infinite number of them.

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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#62 2012-10-23 08:38:00

zetafunc.
Guest

Re: Laplace Transform of tan(t)

bobbym wrote:

Hi haron;

The transform of that does exist.

Welcome to the forum!

Is that supposed to be the Euler-Mascheroni constant? Where is that coming from?

#63 2012-10-23 08:47:22

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

Re: Laplace Transform of tan(t)

Hi;

This was long ago and needs refreshing. That either comes from Alpha or a table. That is the Euler-Mascheroni constant.

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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#64 2012-10-23 10:35:34

zetafunc.
Guest

Re: Laplace Transform of tan(t)

W|A is giving me that but without that constant. Can't really see where it would come from... I'll try the integration tomorrow.

#65 2012-10-23 10:41:41

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

Re: Laplace Transform of tan(t)

Hi;

Alpha is not quite up to the stand alone program.

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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#66 2012-10-23 10:42:33

zetafunc.
Guest

Re: Laplace Transform of tan(t)

I don't have the money for it yet.

#67 2012-10-23 10:47:29

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

Re: Laplace Transform of tan(t)

Make sure you scan it well.

Probably that constant comes from the fact that the answer contains a series that equals it.

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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#68 2012-10-23 10:54:47

zetafunc.
Guest

Re: Laplace Transform of tan(t)

Off the top of my head I can only think of the sum of the reciprocals of the natural numbers from 1 to n, minus log(n), as n tends to infinity. I know that yields the Euler-Mascheroni constant. I do not know of any others, maybe there are more.

#69 2012-10-23 10:58:03

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

Re: Laplace Transform of tan(t)

Oh yes, there are many more! But no one knows whether it is irrational or 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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#70 2012-10-23 11:06:18

zetafunc.
Guest

Re: Laplace Transform of tan(t)

Really? I did not know that. I just assumed it was irrational...

#71 2012-10-23 11:08:40

zetafunc.
Guest

Re: Laplace Transform of tan(t)

The constant also comes out in the Laplace transform of natural log. Interesting.

#72 2012-10-23 11:15:47

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

Re: Laplace Transform of tan(t)

You should like this one:

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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#73 2012-10-23 11:17:30

zetafunc.
Guest

Re: Laplace Transform of tan(t)

Haha, it is the Zeta function! I am going to make a note of that one. I wonder how that can be proven.

#74 2012-10-23 11:19:21

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

Re: Laplace Transform of tan(t)

Hi;

I do not remember but if I see it...

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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#75 2012-10-23 11:21:01

zetafunc.
Guest

Re: Laplace Transform of tan(t)

I am looking at the wiki page now. There are lots involving the gamma function.