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You are not logged in. #51 20110718 23:47:20
Re: Tricky integral of a rational functionHi;
Then we have a major problem here because I have no idea what they are doing either. 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. #52 20110719 00:04:02
Re: Tricky integral of a rational functionThe whole transformation thing is crazy! "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." #53 20110719 11:22:06
Re: Tricky integral of a rational functionHi; These are the poles ( the roots of the denominator), that lie in upper half of the contours plane? These are the residues of the poles. Sum them and times by 2 π i and you get: Which is very close to just π. We divide it by two because our integral is symmetrical and goes from 0 to infinity. Now we can see that unless we can get the poles analytically we will not get anything but a numerical answer. Since the denominator is a 12th degree polynomial there is no algebraic method to extract the roots ( poles ) so even a package is forced to go to numerics to get them. So if anyone can get this integral analytically I would say he would have to first reduce the denominator to a combination of quartics. 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. #54 20110719 18:19:42
Re: Tricky integral of a rational functionhi bobbym, Last edited by bob bundy (20110719 18:21:02) You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei #55 20110719 20:50:16
Re: Tricky integral of a rational functionHi Bob; 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. #56 20110719 20:58:05
Re: Tricky integral of a rational functionHi, "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." #57 20110719 21:05:18
Re: Tricky integral of a rational functionHi gAr; 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. #58 20110719 21:21:51
Re: Tricky integral of a rational functionHi 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." #59 20110719 21:23:36
Re: Tricky integral of a rational functionHi gAr; 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. #60 20110719 21:37:56
Re: Tricky integral of a rational functionOkay. "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." #61 20110720 01:20:55
Re: Tricky integral of a rational functionhi bobbym and gAr then the next four are and the final four are Not quite what I was hoping for after 11 months of trying, but I had to post something. Bob You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei #62 20110720 02:03:07
Re: Tricky integral of a rational functionHi Bob, "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." #63 20110720 02:59:50
Re: Tricky integral of a rational functionHi Bob;
Yes, we could do that. But we would end up with cofficients that were approximations. 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. #64 20110720 03:11:43
Re: Tricky integral of a rational functionHi 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." #65 20110720 03:17:29
Re: Tricky integral of a rational functionHi gAr; 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. #66 20110720 03:31:16
Re: Tricky integral of a rational functionOkay. "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." #67 20110720 18:41:49
Re: Tricky integral of a rational functionHi 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. #69 20110722 05:43:41
Re: Tricky integral of a rational function
Hi guys, I'm sorry to revive this thread  which I'm sure you would like to put to bed  but I was following this thread out of interest. The link which bobbym provided is fascinating  if probably far beyond me, but something which I think is within my grasp  and yet which, at the moment, I can't follow  is this. I wonder if anybody could be so kind as to explain why this is the case, I can see that: But I was unsure about the two numerators. I think I recall partial fractions being mentioned in this thread and this does remind me of a partial fraction  albeit an incredibly complicated one  but I've only ever had integers as numerators, and when I tried my method, I was at a loss as to how to reproduce this result. Of course, I wouldn't have been able to factorise: Either  I merely verified that it was the case on a piece of paper. I think what I really want to do is to understand why this holds, even if I couldn't derive it myself, I think that that might be a bit beyond me. So what I'm asking is why are the two numerators what they are? Thanks #70 20110722 06:07:01
Re: Tricky integral of a rational functionHi Au101; 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. #71 20110722 06:14:17
Re: Tricky integral of a rational functionWow, I see, okay thanks bobbym, I was just interested mainly in a quick look at the proof and I agree that I don't think there's much that a human could do with a pen and paper, but since you seemed to have got that factorisation yourself I was wondering if I could verify it for myself and quickly failed . #72 20110722 06:15:58
Re: Tricky integral of a rational functionHi Au101; 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. #73 20110722 06:44:55
Re: Tricky integral of a rational functionOh, well, what I did was  mainly for my own satisfaction  to expand Which of course gives a massive expansion, if it's of interest: Which, when you add it all together gives: Which, of course, is: So I had satisfied myself with the denominators and I tried using my standard partial fractions method and said But then I got: And gave up, because I knew that I must have been on the wrong track. And, well, that's when I asked you lol Last edited by Au101 (20110722 06:50:17) #74 20110722 06:50:55
Re: Tricky integral of a rational functionHi; 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. #75 20110722 06:56:54
Re: Tricky integral of a rational functionHmmm, I can definitely do 2) in theory  although that's not to say that I might not have some trouble with doing a large, difficult, practical example  although I should think I would probably enjoy trying and, well, as for 1) I not only know the form, I know what they are, since I wish only to verify it, as much as I would like to be able to derive something like this  not being a computer  or at least an extremely experienced and intelligent professor of advanced mathematics  I think that to do so may well be somewhere beyond me. 