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You are not logged in. #1 20110806 18:21:10
Getting an asymptotic form for a GF.Hi Supposing we wished to know what a was in: We could form a recurrence, we could expand out g(x) with a computer, we could get the Taylor series of a few terms of g(x) and hope to spot a pattern. Or we could try to get an asymptotic expression for the coefficients of a. Here is how to do it with the help of a CAS. Start by getting the Laurent expansion for g(x): Now we expand L(x) around 0. Substitute x = 1 to form a sequence. Fit a function to the above values. In this case a 4th degree polynomial was tried and found to be okay. Now we have an asymptotic form for the coefficients of g(x)! Plug in 1000000 That should be a very good approximation to the exact answer 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. #2 20110806 18:44:26
Re: Getting an asymptotic form for a GF.Hi bobbym, "Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  Buddha? "Data! Data! Data!" he cried impatiently. "I can't make bricks without clay." #3 20110806 18:53:18
Re: Getting an asymptotic form for a GF.Hi gAr; 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. #4 20110806 18:57:07
Re: Getting an asymptotic form for a GF.Hi, "Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  Buddha? "Data! Data! Data!" he cried impatiently. "I can't make bricks without clay." #5 20110806 19:01:05
Re: Getting an asymptotic form for a GF.Hi gAr; 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. #6 20110806 19:24:12
Re: Getting an asymptotic form for a GF.Hi bobbym, Close to your approximation, so I hope it's correct. "Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  Buddha? "Data! Data! Data!" he cried impatiently. "I can't make bricks without clay." #7 20110806 19:29:18
Re: Getting an asymptotic form for a GF.Hi gAr; 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. #8 20110806 19:35:39
Re: Getting an asymptotic form for a GF.Hi, "Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  Buddha? "Data! Data! Data!" he cried impatiently. "I can't make bricks without clay." #9 20110806 19:59:23
Re: Getting an asymptotic form for a GF.Hi gAr; 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. #10 20110806 20:03:11
Re: Getting an asymptotic form for a GF.Hi bobbym, "Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  Buddha? "Data! Data! Data!" he cried impatiently. "I can't make bricks without clay." #11 20110806 20:06:33
Re: Getting an asymptotic form for a GF.Hi gAr; 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 20110806 20:11:58
Re: Getting an asymptotic form for a GF.Hi, "Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  Buddha? "Data! Data! Data!" he cried impatiently. "I can't make bricks without clay." #13 20110806 20:21:40
Re: Getting an asymptotic form for a GF.Hi gAr; 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. #14 20110806 20:35:43
Re: Getting an asymptotic form for a GF.Hi bobbym, "Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  Buddha? "Data! Data! Data!" he cried impatiently. "I can't make bricks without clay." #15 20110806 20:57:15
Re: Getting an asymptotic form for a GF.Hi gAr; 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. #16 20110806 20:59:48
Re: Getting an asymptotic form for a GF.Hi bobbym, "Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  Buddha? "Data! Data! Data!" he cried impatiently. "I can't make bricks without clay." #17 20110806 21:03:26
Re: Getting an asymptotic form for a GF.Hi gAr; 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. #18 20110806 21:06:15
Re: Getting an asymptotic form for a GF.Okay, no problem. "Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  Buddha? "Data! Data! Data!" he cried impatiently. "I can't make bricks without clay." #19 20110806 21:16:12
Re: Getting an asymptotic form for a GF.Hi gAr; 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. #20 20110806 21:36:09
Re: Getting an asymptotic form for a GF.Hi bobbym, "Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  Buddha? "Data! Data! Data!" he cried impatiently. "I can't make bricks without clay." #21 20110806 21:40:20
Re: Getting an asymptotic form for a GF.Hi; 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. #22 20110806 21:46:20
Re: Getting an asymptotic form for a GF.Hi bobbym, "Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  Buddha? "Data! Data! Data!" he cried impatiently. "I can't make bricks without clay." #23 20110806 21:57:27
Re: Getting an asymptotic form for a GF.Hi gAr; You need the coefficient of x^10 Which is correct without the i. 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. #24 20110806 22:03:57
Re: Getting an asymptotic form for a GF.Hi bobbym, "Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  Buddha? "Data! Data! Data!" he cried impatiently. "I can't make bricks without clay." #25 20110806 22:06:42
Re: Getting an asymptotic form for a GF.Hi; 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. 