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You are not logged in. #9401 20130323 00:24:51
Re: Linear Interpolation FP1 FormulaBut it looks so tedious to find the residues... #9402 20130323 00:33:02
Re: Linear Interpolation FP1 FormulaI am getting: 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. #9403 20130323 00:37:18
Re: Linear Interpolation FP1 FormulaThat is correct... did you use the residues? #9404 20130323 00:38:06
Re: Linear Interpolation FP1 FormulaYes, there is a simple formula for computing them when the poles are simple. 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. #9405 20130323 00:38:34
Re: Linear Interpolation FP1 FormulaWhat formula? #9406 20130323 00:40:12
Re: Linear Interpolation FP1 FormulaI am the worst at definitions so please check this. I think a simple pole is a pole with multiplicity of 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. #9407 20130323 00:43:52
Re: Linear Interpolation FP1 FormulaI'm not sure what you mean by the pole having a multiplicity of one... #9408 20130323 00:45:21
Re: Linear Interpolation FP1 FormulaMultiplicity of one means there is only one pole like that. Of two, would mean two poles the same. 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. #9409 20130323 00:49:51
Re: Linear Interpolation FP1 FormulaYes but I don't understand how two poles can be the same... how do you mean? #9410 20130323 00:51:32
Re: Linear Interpolation FP1 FormulaIf the roots of the denominator are all different then the poles are all simple ones because they are of order 1. 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. #9411 20130323 00:53:25
Re: Linear Interpolation FP1 FormulaOhh I see, so it is sort of like having repeated roots of a polynomial? #9412 20130323 00:55:06
Re: Linear Interpolation FP1 FormulaYes, something like that. It may be more complicated and I do not remember. But for our purposes that integral has 4 simple poles. We are interested in only two. The formula becomes very, very easy when the pole is simple. Last edited by bobbym (20130323 00:55:32) 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. #9413 20130323 01:03:08
Re: Linear Interpolation FP1 FormulaAre you using this formula? I cannot get the formula to display properly, it is the one with the limit of z > z_{0}, and the derivative and the factorial. #9414 20130323 01:04:05
Re: Linear Interpolation FP1 FormulaHi; Last edited by bobbym (20130323 01:05:24) 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. #9415 20130323 01:13:05
Re: Linear Interpolation FP1 FormulaIs there some sort of bug with the latex today, I have tried to type 3 formulae and none of them worked apart from a few...? #9416 20130323 01:21:51
Re: Linear Interpolation FP1 FormulaHi; n is the order of the pole. a is the pole. Add that for each pole and then times by 2πi 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. #9417 20130323 01:27:01
Re: Linear Interpolation FP1 FormulaYes, that is the formula I am using. But how do you use it? How would you then use your formula to find the residue? #9418 20130323 01:28:05
Re: Linear Interpolation FP1 FormulaLet's continue with the other one first. I will post the answer step by step. 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. #9419 20130323 01:31:12#9420 20130323 01:43:37
Re: Linear Interpolation FP1 FormulaWe need two: n = 1 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. #9421 20130323 01:54:58#9422 20130323 02:01:09
Re: Linear Interpolation FP1 FormulaThe limits? L'Hopitals rule and Alpha for the plugging in. 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. #9423 20130323 02:19:04
Re: Linear Interpolation FP1 FormulaI am not getting your answer... I am ending up with #9424 20130323 02:30:25
Re: Linear Interpolation FP1 FormulaWhat did you get for the first limit? 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. #9425 20130323 02:50:15 