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You are not logged in. #9376 20130321 22:56:18
Re: Linear Interpolation FP1 FormulaHi; Last edited by bobbym (20130321 23:09:01) 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. #9377 20130321 23:33:34
Re: Linear Interpolation FP1 FormulaI looked up a handout, apparently you just take the reciprocal of z^n and sum it... #9378 20130322 00:19:05
Re: Linear Interpolation FP1 FormulaDo you have the link? 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. #9379 20130322 00:23:26
Re: Linear Interpolation FP1 FormulaGoogle "calculating laurent series" and click on the first link, titled "[PDF] 1 What is a Laurent series? 2 Calculating the Laurent series..." #9380 20130322 00:33:16
Re: Linear Interpolation FP1 FormulaI see your problem there but how is that answer the Laurent series. It has no principal part! Last edited by bobbym (20130322 00:41:00) 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. #9381 20130322 00:34:01#9382 20130322 00:39:21
Re: Linear Interpolation FP1 FormulaThe part of a Laurent series that has the terms involving negative exponents. 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. #9383 20130322 00:40:57
Re: Linear Interpolation FP1 FormulaAccording WA there was a 1/(z  a) term... #9384 20130322 00:45:57
Re: Linear Interpolation FP1 FormulaOn the last page they give, but it has no negative exponent. Oh boy! It is staring me right in the face, I am sorry. Last edited by bobbym (20130322 00:48:10) 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. #9385 20130322 02:30:05
Re: Linear Interpolation FP1 FormulaYes, that one has negative powers of z. #9386 20130322 02:36:59
Re: Linear Interpolation FP1 FormulaI have some examples of how to do contour integrals but my understanding of the theory is not good. 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. #9387 20130322 02:39:31#9388 20130322 02:43:27
Re: Linear Interpolation FP1 FormulaA couple of hopefully not too difficult ones. They were easier back when I did them, now they might be impossible. 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. #9389 20130322 02:48:34
Re: Linear Interpolation FP1 FormulaHopefully it will not look like Greek to me... (in which case, I can just get adriana to help) #9390 20130322 02:52:34
Re: Linear Interpolation FP1 FormulaIf you have one to post go right ahead. Or do you want me to post 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. #9391 20130322 02:56:30
Re: Linear Interpolation FP1 FormulaI thought you were going to post one  I would like to see one of your examples, if possible, thanks. #9392 20130322 03:03:08
Re: Linear Interpolation FP1 FormulaHow about this 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. #9393 20130322 23:03:46
Re: Linear Interpolation FP1 FormulaWould it be appropriate to use partial fractions with imaginary coefficients here, to generate the Laurent series? #9394 20130322 23:18:38
Re: Linear Interpolation FP1 FormulaHi; Since we are going from 0 to ∞ we only take the second and fourth poles. Are we okay up to here? 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. #9395 20130322 23:25:35
Re: Linear Interpolation FP1 FormulaUsing Cauchy's integral formula I got the wrong answer... I said Let the contour enclose the part of the plane from 0 to infinity, so only sqrt(i) is the pole included in the contour, right? Then Cauchy's integral formula says: Letting n = 1, a = sqrt(i) gives me: evaluated at z = sqrt(i) gives me an answer of pi/2... but the correct answer is I am stuck.  Sorry, just saw your post. Okay that makes sense, we use those two poles since they are in our region of interest (the real integral doesn't exist below the axis, where the other poles are). #9396 20130322 23:41:49
Re: Linear Interpolation FP1 FormulaHi;
Post #9394, there are two poles. The positive ones count. 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. #9397 20130323 00:00:52
Re: Linear Interpolation FP1 FormulaOkay, so that means we are taking two contours? #9398 20130323 00:08:41
Re: Linear Interpolation FP1 FormulaMaybe there are conditions for the Cauchy integral that are being violated. 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. #9399 20130323 00:19:19
Re: Linear Interpolation FP1 FormulaI tried again and no division by zero, but I'm getting which is obviously wrong... #9400 20130323 00:23:08
Re: Linear Interpolation FP1 FormulaMaybe we can work this with this formula here for the residues it looks easy. 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. 