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You are not logged in. #1 20110813 01:13:25
Laplace Transform of tan(t)Hello, I've started to approach the problem differently by using the definition of tan(t); and I'm just trying to integrate that at the moment and I've ended up with some more complicated integrals after using integration by parts. I was wondering what your thoughts on this are and if this is a step in the right direction, or just a push in which direction I should go next. One question I have though is if this even makes sense... in that, using the definition of the Laplace transform, the integral is divergent in the first place. So how does WolframAlpha get an answer, and will my method of using the definition of tan(t) in terms of e and i work? Thanks. #2 20110813 01:38:41
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. #3 20110813 01:43:43
Re: Laplace Transform of tan(t)I'm entering "Laplace transform of tan(t)". #4 20110813 01:48:24
Re: Laplace Transform of tan(t)May I have the exact way you are entering it. Because I am timing out in Alpha and at home. 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. #5 20110813 02:03:28
Re: Laplace Transform of tan(t)I'm entering "Laplace transform of tan(t)" and getting that. What's in the quotes is what I'm entering... #6 20110813 02:10:45
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. #7 20110813 02:13:11
Re: Laplace Transform of tan(t)Laplace transform of t just brings up a bunch of text, but entering "Laplace transform of sin(t)" or "Laplace transform of cos(t)" gives the right answer as a function of s. #8 20110813 02:14:18
Re: Laplace Transform of tan(t)It can do Laplace transform of t if you enter "Laplace transform of (t)" but not "Laplace transform of t". I think you have to encase it in brackets. #9 20110813 02:23:50
Re: Laplace Transform of tan(t)Is that not the most squirrely thing I have ever seen? 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. #10 20110813 02:26:01
Re: Laplace Transform of tan(t)Nope, sorry... I asked on another forum and they don't seem to know either. I'm not sure what to do because it's an interesting problem especially given what WolframAlpha spat out, what with the digamma function being there... #11 20110813 02:30:05
Re: Laplace Transform of tan(t)That is the problem, that is not an elementary function. It is not likely that hand methods are going to get that answer. 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. #13 20110813 02:39:57
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. #14 20110813 02:44:25
Re: Laplace Transform of tan(t)Hi, But I don't know for now whether it matches with the wolfram's output. I'll continue trying for some more time! "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." #15 20110813 02:47:42
Re: Laplace Transform of tan(t)Okay... #16 20110813 02:49:56
Re: Laplace Transform of tan(t)Check what gAr did it might be your only hope. 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. #17 20110813 02:50:25
Re: Laplace Transform of tan(t)
Thanks for this, can you talk me through how you found that series? #18 20110813 03:01:10
Re: Laplace Transform of tan(t)Hi zetafunc., Put that in the integral and integrate term by term... Now we need to check what would be the expansion for the wolfram's output. The output was instantaneous, looked like a cached result! edit: I read #15 again, now I doubt WA's output, as well as mine! And cannot find it in any table also. So, may not exist. Last edited by gAr (20110813 03:08:44) "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." #19 20110813 03:17:36
Re: Laplace Transform of tan(t)Hi all; 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. #20 20110813 03:38:57
Re: Laplace Transform of tan(t)Thanks for the replies. I like gAr's method of finding a series then integrating each term. #21 20110813 03:42:15
Re: Laplace Transform of tan(t)Only thing is it cannot reduce it to an elementary form. If the transform does not exist then it does not exist. 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. #22 20110813 03:45:31
Re: Laplace Transform of tan(t)Someone on another forum started talking about Cauchy principle value integrals and converting a Lebesgue divergent integral (this one) into a Cauchy principle value integral to get the Laplace transform, but I don't know how to do that and I'm trying to make sense of the Wikipedia article. #23 20110813 03:46:26
Re: Laplace Transform of tan(t)Hi bobbym, "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." #24 20110813 03:52:11
Re: Laplace Transform of tan(t)I just took a look at the graph of the digamma function and it does look very very similar for negative integer values of x... there probably is a connection. The positive side of the graph looks nothing like that though. #25 20110813 04:01:18
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. 