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You are not logged in. #1 20110505 18:01:38
Generating recurrences from generating functions.Hi Into a recurrence. One that would allow us to find the coefficients without expanding. The act of taking the log of g(x) and then differentiating it would result in linearizing the gf. I can no longer remember what my method was but I do still have the program that does it for me. The next best thing is a general formula for this type problem. Let us run a few test cases and in the best use of experimental math, see if we can spot a pattern. Proof comes later. yields the recurrence: yields the recurrence: yields the recurrence: yields the recurrence: Seems like a pattern has developed. yields the recurrence: So doing the simple: From the above formula: Filling in for the variables: 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 20110505 19:18:48
Re: Generating recurrences from generating functions.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 20110505 19:23:45
Re: Generating recurrences from generating functions.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 20110505 19:42:30
Re: Generating recurrences from generating functions.Okay, I'll remember. "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 20110506 04:26:10
Re: Generating recurrences from generating functions.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." #6 20110506 12:30:13
Re: Generating recurrences from generating functions.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. #7 20110506 12:53:41
Re: Generating recurrences from generating functions.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." #8 20110506 13:01:42
Re: Generating recurrences from generating functions.The method is useful at times. Sometimes even a package has trouble getting them. For instance: If you needed something like the coefficient of x^224 519, a recursion is convenient. Using expand is package abuse. 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 20110506 13:10:51
Re: Generating recurrences from generating functions.Yes, that's true! "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." #10 20110506 13:19:47
Re: Generating recurrences from generating functions.Even better at times is an asymptotic answer. These require a bit more math but save a ton of computation. 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. #11 20110506 13:33:57
Re: Generating recurrences from generating functions.Okay, but I have never used an asymptotic approximations. "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." #12 20110506 13:55:10
Re: Generating recurrences from generating functions.I will bet you have. Ever used Stirlings formula or the HardyRamanujan 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. #13 20110506 14:07:41
Re: Generating recurrences from generating functions.Yes, I have used. I actually wanted to say I never derived any. "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." #14 20110506 15:03:58
Re: Generating recurrences from generating functions.They are pretty tough. It is a big field all by itself. I can do a little bit of it. 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. 