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You are not logged in. #26 20110813 04:03:54
Re: Laplace Transform of tan(t)Yes, that's what I observed too... "Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  Buddha? "Data! Data! Data!" he cried impatiently. "I can't make bricks without clay." #27 20110813 04:16:03
Re: Laplace Transform of tan(t)Also there is a Inverse Laplace Transform that could be tried on that answer. 5 to 1 says it does not return tan(t). In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #28 20110813 04:25:37
Re: Laplace Transform of tan(t)Yes, bur I'll not try that! "Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  Buddha? "Data! Data! Data!" he cried impatiently. "I can't make bricks without clay." #29 20110813 04:27:33
Re: Laplace Transform of tan(t)
Posted here if you might find it useful. If this is true then the Inverse Laplace transform of that function won't return tan(t)... #30 20110813 04:34:46
Re: Laplace Transform of tan(t)That is almost like Borel summation. Some Sums that diverge ( Ramanujan sums ) converge in a Borel sense. In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #31 20110813 04:40:29
Re: Laplace Transform of tan(t)What I want to know though is how you can change the integral so that it does not diverge... #32 20110813 04:41:23
Re: Laplace Transform of tan(t)Hmmm, okay. "Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  Buddha? "Data! Data! Data!" he cried impatiently. "I can't make bricks without clay." #33 20110813 04:41:37
Re: Laplace Transform of tan(t)Simplest way might be by truncating it. But why? It would not be the Laplace Transform. In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #34 20110813 04:45:08
Re: Laplace Transform of tan(t)You mean a Laplace transform such that the transform is valid for some interval [a,b] provided that the interval does not contain any singularities? That might work but I agree it would not be the Laplace transform. Is there a way you can do it without including any singularities? #35 20110813 04:48:20
Re: Laplace Transform of tan(t)Hi zetafunc.; In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #36 20110813 04:48:37
Re: Laplace Transform of tan(t)I have a whiteboard at home and on it still has written the result of performing integration by parts twice on tan(t) defined in terms of e and i. #37 20110813 04:49:52
Re: Laplace Transform of tan(t)Yes, move the i right through it is a constant. In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #38 20110813 04:51:34
Re: Laplace Transform of tan(t)Do you know anything about Cauchy principal values? As you said it is similar to Borel sums where you can turn a diverging summation into a converging one that can hold true for all values. #39 20110813 04:54:43
Re: Laplace Transform of tan(t)Thanks, I can get on with performing another IBP now now that I know factoring out the i is okay... #40 20110813 04:55:03
Re: Laplace Transform of tan(t)Hi; In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #41 20110813 04:56:58
Re: Laplace Transform of tan(t)Borel summations are used by physicists? Hmm... what would they use them for? (sorry for going offtopic) #42 20110813 05:01:24
Re: Laplace Transform of tan(t)Never mind, found it:
#43 20110813 05:02:02
Re: Laplace Transform of tan(t)As near as I understand it was convenient for certain series that diverged to be convergent for quantum mechanics. I do not know any more about that. Except that using Borel summation a sequence of positive numbers when added, can sum to a negative number! In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #44 20110813 05:04:43
Re: Laplace Transform of tan(t)Thanks for the reply  are you saying that Borel summation can mean a sequence of positive numbers can sum to a negative number? #45 20110813 05:05:48
Re: Laplace Transform of tan(t)Maybe I should post the problem on lots of other forums, no one seems to be responding on PF. Maybe someone knows how to apply Cauchy principal values here... #46 20110813 05:14:42
Re: Laplace Transform of tan(t)You could do that but remember you can not force this one to have the answer you want. It will always come up the same, divergent. In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #47 20110813 05:15:34
Re: Laplace Transform of tan(t)
Ramanujan did a couple of sums like that. In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #48 20110814 01:37:52
Re: Laplace Transform of tan(t)Still no luck with converting it to a Cauchy principal value integral... I'm not sure how to set it up because tan(t) is periodic with singularities every interval of π. Do you think I could work backwards from WA's result and see where that gets if I calculate the inverse Laplace transform of that by hand? I know I shouldn't completely trust Wolfram Alpha's result but the direction that this problem has taken interests me as I didn't think you could find a way to define the Laplace transform for a nonpiecewise continuous periodic function... #49 20110814 01:47:03
Re: Laplace Transform of tan(t)Hi; In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #50 20110814 01:54:39
Re: Laplace Transform of tan(t)Well, I'll never know until I try... I don't know how to use a computer to do it either, and taking the inverse Laplace transform of all those digamma functions looks sticky. 