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You are not logged in. #8251 20130222 11:31:28
Re: Linear Interpolation FP1 FormulaHi; 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. #8252 20130222 11:40:47
Re: Linear Interpolation FP1 FormulaI'm confused how you got that... how are you getting that? #8253 20130222 11:44:24
Re: Linear Interpolation FP1 FormulaRepeated integration by parts is how that is generated. Most asymptotic series are generated by IBP. 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. #8254 20130222 11:58:53
Re: Linear Interpolation FP1 FormulaJust tried it, I get the same answer. That is cool, I always thought that if you got an infinite series through IBP it was just poor form. I will try this with some other integrals... #8255 20130222 12:01:31
Re: Linear Interpolation FP1 FormulaSometimes IBP will get the integral exactly, as you have seen. Sometimes it can get an asymptotic form like the one above. Sometimes it can get an ordinary power series. Each one has uses if used correctly. 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. #8256 20130222 12:06:45
Re: Linear Interpolation FP1 FormulaYou will get an asymptotic form for the integral of sinx / x too, right? (through repeated IBP) #8257 20130222 12:14:44
Re: Linear Interpolation FP1 FormulaYes, that is an asymptotic form for any x. Last edited by bobbym (20130222 14:20:15) 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. #8258 20130222 21:17:09#8259 20130223 02:33:04
Re: Linear Interpolation FP1 FormulaTo compute with them you only use a finite number of terms rather than an infinite number like with a power series. 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. #8260 20130223 02:56:14
Re: Linear Interpolation FP1 FormulaBecause the terms quickly get relatively smaller enabling you to justify the accuracy of your sum? #8261 20130223 03:14:40
Re: Linear Interpolation FP1 FormulaYes, continu3d fractions is nice for approximating constants and they also solve pell equations.
You keep using the terms that are getting smaller. The first term that gets larger you stop there. 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. #8262 20130223 03:23:29
Re: Linear Interpolation FP1 FormulaYes, I remember, using the convergents. I think you showed me a post of yours about it... #8263 20130223 03:30:21
Re: Linear Interpolation FP1 FormulaThat is what I meant. The term right before that one. 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. #8264 20130223 03:35:58
Re: Linear Interpolation FP1 FormulaOh, okay. Also, I have a question about continued fractions again. About 4 months ago you told me that the continued fraction of root 11 was {3; 3, 6, 3, 6, 3, 6, ...} with period 2. But the numerators must be 1 so I just divided through by 5 to get 0.2 for each quotient apart from the zeroth one. Can you show me how you got a different continued fraction? Is mine not valid? It is a problem because I am getting different convergents, so I cannot solve Pell equations with my current method. #8265 20130223 03:41:03
Re: Linear Interpolation FP1 FormulaThat is not the continued fraction for 11. 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. #8266 20130223 03:51:49
Re: Linear Interpolation FP1 Formulaso Where am I going wrong, if I truncate it after a bit it seems to converge well? #8267 20130223 04:13:24
Re: Linear Interpolation FP1 FormulaHi; 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. #8268 20130223 04:14:17
Re: Linear Interpolation FP1 FormulaCould you show me how you got your continued fraction? #8269 20130223 04:18:22
Re: Linear Interpolation FP1 FormulaDo you remember the algorithm I showed you? 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. #8270 20130223 04:24:24
Re: Linear Interpolation FP1 FormulaYes, but it is impractical without a calculator/CAS... #8271 20130223 04:31:00
Re: Linear Interpolation FP1 FormulaThe method used in post #8266 seems okay but much more difficult than with a calculator. 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. #8272 20130223 04:39:04
Re: Linear Interpolation FP1 FormulaI should really learn to like calculators... #8273 20130223 04:50:47
Re: Linear Interpolation FP1 FormulaTo answer that I suggest you do another √19.
Yes!!!!!! If you hope to get to CERN or any other installation in the world they will demand you use a calculator or a CAS. Start now, especially since there is someone around to teach you. 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. #8274 20130223 04:57:18
Re: Linear Interpolation FP1 FormulaThe convergence will probably be slower for larger numbers, but from my method, doesn't it follow that where p is prime? So for your example p = 19... I guess I don't mind calculators but I've never used a CAS before, I don't think. Aside from WolframAlpha or something... as for CERN, I don't know if I want to do that. That was back when I loved physics... at the moment I'm undecided. #8275 20130223 05:05:07
Re: Linear Interpolation FP1 FormulaActually ignore the 'p is prime' comment, that is irrelevant... 