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You are not logged in. #1926 20130929 11:16:49
Re: Is this cool with you?Recursion in my opinion is rarely the best way to go. 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. #1927 20130929 17:38:43
Re: Is this cool with you?Okay, what now? The limit operator is just an excuse for doing something you know you can't. “It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman “Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment #1928 20130929 19:49:55
Re: Is this cool with you?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. #1929 20131001 04:26:19
Re: Is this cool with you?Hi Code:romberg[l_] := Module[{x, a}, a = Dimensions[l][[1]]; x = 1/2; Clear[f]; f[n_, 1] := f[n, 1] = l[[n]]; f[i_, j_] := f[i, j] = (f[i, j  1]  x^(j  1)*f[i  1, j  1])/(1  x^(j  1)); f[a, a]]; Hm, let me try it on another one. The limit operator is just an excuse for doing something you know you can't. “It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman “Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment #1930 20131001 04:33:48
Re: Is this cool with you?Did you write 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. #1931 20131001 04:36:00
Re: Is this cool with you?Write what? The limit operator is just an excuse for doing something you know you can't. “It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman “Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment #1932 20131001 04:39:52
Re: Is this cool with you?That Romberg or all of Shakespeare? 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. #1933 20131001 04:44:12
Re: Is this cool with you?I wrote the romberg function. Why? The limit operator is just an excuse for doing something you know you can't. “It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman “Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment #1934 20131001 04:46:46
Re: Is this cool with you?That is good. Did you get the point of it in post 1928? 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. #1935 20131001 04:48:31
Re: Is this cool with you?Hi Last edited by anonimnystefy (20131001 04:49:44) The limit operator is just an excuse for doing something you know you can't. “It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman “Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment #1936 20131001 04:56:39
Re: Is this cool with you?Yes, I am familiar with memoization. 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. #1937 20131001 05:00:20
Re: Is this cool with you?Code:Table[Sum[(11 i + 6)/(i^3 (i + 1) (i + 2) (i + 3)), {i, 1, n}], {n, 1, 50}]; N[romberg1[%], 30] 0.785389896574820021713652114058 5/12 + %  Zeta[3] 3.39918107597019419380786*10^7 Last edited by anonimnystefy (20131001 05:01:25) The limit operator is just an excuse for doing something you know you can't. “It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman “Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment #1938 20131001 05:10:18
Re: Is this cool with you?Sequence acceleration has rules and the tail does not apply. 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. #1939 20131001 05:11:27
Re: Is this cool with you?Could you elaborate? The limit operator is just an excuse for doing something you know you can't. “It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman “Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment #1940 20131001 05:13:11
Re: Is this cool with you?Notice how I constructed s. 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. #1941 20131001 05:16:23
Re: Is this cool with you?Sequences that are decreasing geometrically and have steep curves seem to accelerate better. The tail is almost flat. 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. #1942 20131001 05:16:49
Re: Is this cool with you?Oh! It goes from 1 to 2^m. I didn't see that one. Sorry! I am getting it now. Thanks! The limit operator is just an excuse for doing something you know you can't. “It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman “Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment #1943 20131001 05:18:21
Re: Is this cool with you?The point is we only needed a couple of terms to get 41 digits. Continuing that table would have required about 10^20. 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. #1944 20131001 05:24:27
Re: Is this cool with you?Yeah, I know. It's a good one. Only about 130 000 is much more doable. The limit operator is just an excuse for doing something you know you can't. “It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman “Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment #1945 20131001 05:25:55
Re: Is this cool with you?Romberg is working fine for about 50 digits but for 100 or so another idea is necessary. 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. #1946 20131001 06:02:39
Re: Is this cool with you?What do you suggest then? The limit operator is just an excuse for doing something you know you can't. “It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman “Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment #1947 20131001 06:08:39
Re: Is this cool with you?I tried shanks, it did not work. 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. #1948 20131001 06:42:30
Re: Is this cool with you?Does any of them work on this one? The limit operator is just an excuse for doing something you know you can't. “It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman “Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment #1949 20131001 07:15:50
Re: Is this cool with you?I do not know yet, as soon as I finish another problem I will start on this 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. #1950 20131002 10:06:32
Re: Is this cool with you?Hi anonimnystefy; it is now easy to get 100+ digits. 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. 