Discussion about math, puzzles, games and fun. Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ • π ƒ ¹ ² ³ °
 

You are not logged in. #9426 20130323 02:53:11
Re: Linear Interpolation FP1 FormulaThat is correct. 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. #9427 20130323 02:58:33#9428 20130323 03:00:18
Re: Linear Interpolation FP1 FormulaThat is correct. 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. #9429 20130323 03:04:41
Re: Linear Interpolation FP1 FormulaAdding and then multiplying by 2*pi*i, I get #9430 20130323 03:12:21
Re: Linear Interpolation FP1 FormulaYou only multiply by π i, see post #9420. 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. #9431 20130323 03:13:47
Re: Linear Interpolation FP1 FormulaWhy? I thought it was 2*pi*i*(sum of the residues), not pi*i... #9432 20130323 03:15:56
Re: Linear Interpolation FP1 FormulaYes, but that is from ∞ to ∞. This integral is symmetrical and goes from 0 to ∞. 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. #9433 20130323 03:24:59
Re: Linear Interpolation FP1 FormulaOh, okay... #9434 20130323 03:32:03
Re: Linear Interpolation FP1 FormulaSomething is wrong with the arithmetic. What are you using to compute the sum of the two limits? 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. #9435 20130323 03:34:15
Re: Linear Interpolation FP1 FormulaHmm, WolframAlpha is getting the right answer, so there is a problem with me, I'll check my arithmetic again. #9436 20130323 03:39:04
Re: Linear Interpolation FP1 FormulaOkay, I am going to have to get some sleep. See you later. You should be able to do some others using this same method. 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. #9437 20130323 05:40:50
Re: Linear Interpolation FP1 FormulaOkay, see you later. #9438 20130323 10:32:48
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. #9439 20130323 10:45:56
Re: Linear Interpolation FP1 FormulaI tried it for something like and I cannot get it to work... #9440 20130323 10:51:16
Re: Linear Interpolation FP1 FormulaWhat did you get for 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. #9441 20130323 11:03:38
Re: Linear Interpolation FP1 FormulaI am getting the residue to be zero but I am guessing I need to do something else... there is only one pole and it is a removable singularity (no C_{1} coefficient in the Laurent series). The answer should be \pi and DUIS can be used to show this, but I wanted to approach it with contour integration. #9442 20130323 11:08:40
Re: Linear Interpolation FP1 FormulaYes, no Laurent series. I am getting zero also. It is obviously wrong so this method might not apply 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. #9443 20130323 11:19:59
Re: Linear Interpolation FP1 FormulaI remember reading some PDF where a guy managed to do it but I can't remember what he did... #9444 20130323 11:27:40
Re: Linear Interpolation FP1 FormulaYes, I believe so. Are you sure you could do it using Residues? This one does not have a Laurent series. Doesn't that mean no poles? 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. #9445 20130323 11:31:54
Re: Linear Interpolation FP1 FormulaBut that function is clearly not defined at x = 0... surely it has a pole there? What else would be there? I thought that if it doesn't appear in the series expansion about that point, then it just means that it is a removable singularity. #9446 20130323 11:34:52
Re: Linear Interpolation FP1 FormulaA pole is the coefficient of the a(1) term. There is no such term 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. #9447 20130323 11:38:40#9448 20130323 11:45:56
Re: Linear Interpolation FP1 FormulaOh excuse me, I meant residue. If the residue is 0 then the integral is 0 according to that formula. 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. #9449 20130323 11:48:45
Re: Linear Interpolation FP1 FormulaBut this integral is π, not zero... what do we do? #9450 20130323 11:50:27
Re: Linear Interpolation FP1 FormulaHave to find another way to evaluate it. What I am saying is that for some reason this method does not apply here. Possibly because it has no Laurent series. Last edited by bobbym (20130323 11:58:33) 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. 