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You are not logged in. #9501 20130325 10:11:22#9502 20130325 10:13:13
Re: Linear Interpolation FP1 FormulaOnce they begin to see you in one of the 9 or 10 forms that they can not do without, then you will do better. 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. #9503 20130325 10:16:44#9504 20130325 10:23:01
Re: Linear Interpolation FP1 FormulaI suggest doing your math and forgetting about them. Not completely but putting them in the last and smallest compartment of your mind. 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. #9505 20130325 23:54:37
Re: Linear Interpolation FP1 FormulaI find it difficult to forget about them... #9506 20130325 23:56:54
Re: Linear Interpolation FP1 FormulaThe tough part of any generating function approach is getting the coefficient. 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. #9507 20130326 00:00:28
Re: Linear Interpolation FP1 FormulaYes, unfortunately no calc/CAS is allowed for STEP. Luckily all I had to do was get the coefficient of x^{24} in (1 + x + x^{2} + x^{3} + x^{4} + x^{5} + x^{6})^{5}. If it was an EGF that would have been more tedious. #9508 20130326 00:06:56
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. #9509 20130326 00:09:41#9510 20130326 00:23:15
Re: Linear Interpolation FP1 FormulaOnly thing it did not have the constant term. 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. #9511 20130326 02:44:06
Re: Linear Interpolation FP1 FormulaSorry, I had to go to school, I am back now. and then just get the coefficient of x^24 from that but then the arithmetic can become a bit long... #9512 20130326 02:45:13
Re: Linear Interpolation FP1 FormulaYou can play spot the pattern. 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. #9513 20130326 02:49:05#9514 20130326 02:55:31
Re: Linear Interpolation FP1 FormulaSupposing you needed the coefficient of x^5 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. #9515 20130326 02:59:56
Re: Linear Interpolation FP1 FormulaBy hand, I think I would just go back to sleep if someone asked me to do that #9516 20130326 03:07:13
Re: Linear Interpolation FP1 FormulaThat could be difficult even by computer. That is when math becomes an art and ceases to be a science. 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. #9517 20130326 03:08:00#9518 20130326 03:19:47
Re: Linear Interpolation FP1 FormulaSometimes in combinatorics we have a big problem. We can often solve it by looking at smaller problems that have the same flavor and then spotting the pattern. For instance it is not too difficult to expand these: What do you notice about the coefficient of x^5 in each case? 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. #9519 20130326 03:25:16
Re: Linear Interpolation FP1 FormulaThe coefficients are constant for the first sequence, (n+1) for the second sequence, and the triangular numbers for the third. #9520 20130326 03:28:41
Re: Linear Interpolation FP1 FormulaYou can put that into a more succinct combinatoric notation. 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. #9521 20130326 03:33:23
Re: Linear Interpolation FP1 Formula(n+1) choose (k1), where k is the power of the big bracket? #9522 20130326 03:38:19#9523 20130326 03:39:34
Re: Linear Interpolation FP1 FormulaYou can phrase wholly in terms of the power n: 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. #9524 20130326 03:46:32
Re: Linear Interpolation FP1 FormulaOh I see. So in my example I could have just done #9525 20130326 03:49:57
Re: Linear Interpolation FP1 FormulaYes, because of symmetry: 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. 