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

You are not logged in. #1 20121031 22:25:37
Laurent Series HelpFind Laurent expansions for: valid in the annuli; (a) 0 ≤ z < 1, (b) 1 < z < 3, (c) 3 < z.  I've found a Laurent expansion but I'm not sure what to do about the different annulus ranges. which forms the geometric series or which I think simplifies to but I don't know how to address the problem of the annulus ranges given for (a), (b) and (c). I think mine is valid for the range in (a), but I don't know what to do about the others. #2 20121101 01:44:12
Re: Laurent Series HelpHi; 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. #3 20121101 01:49:29
Re: Laurent Series HelpI know those are the poles (from the quadratic), but how can I use that here? I thought the principal part was the part of the series involving negative powers  which part is my principal part here? #4 20121101 02:02:52
Re: Laurent Series HelpThe principle part is the part involving negative powers. To find the Laurent you expand around one of the poles. Which pole did you use? 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. #5 20121101 02:16:18
Re: Laurent Series HelpI'm not sure what you mean  I just got f(z) into a form which I could generate the series of. How do I expand around a pole? #6 20121101 02:33:57
Re: Laurent Series HelpHi; 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. #7 20121101 02:36:31
Re: Laurent Series HelpI don't know. The lecture notes I am looking at say "find Laurent expansions for the function f(z)" and gives the annulus ranges. #8 20121101 02:52:57
Re: Laurent Series HelpI can get two Laurent series for that but I do not remember how to handle the annulus stuff. I did not write it down either so I will have to rediscover the 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. #9 20121101 02:56:59
Re: Laurent Series HelpGo here: #10 20121101 03:10:34
Re: Laurent Series HelpHi; 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. #12 20121101 03:37:34
Re: Laurent Series HelpHi; 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. 