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You are not logged in. #1 20120720 12:04:15
A Development of New Numerical Analysis MethodI have developed new method for Numerical Analysis for sums of power for arithmetic progression of noninteger power and still working on it to improve its accuracy. However, before I could present it, has anybody got an idea how to sum this series . Is there any formulation that could sum it?Last edited by Stangerzv (20120720 12:11:17) #2 20120720 15:48:55
Re: A Development of New Numerical Analysis MethodHi Stangerzv; 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 20120720 22:17:12
Re: A Development of New Numerical Analysis MethodThanks bobbym for the info. I have developed two ways of finding the sums, first method is using Area Integration which gives quite high error. Another one is using unbounded sums of power of arithmetic progression. After using 4 internal coefficients I managed to get 0.004% Error. As the internal coefficients reach infinity the sum will approach 100% accuracy. Can you show me the closed form formulation? As to my knowledge, if the closed form for this series existed then the sums of power for arithmetic progression would be technically found ages ago. There is a paper on the sums of power formulation by Chen et al dated 2008 and accepted by 2010, you can read their paper by the title Faulhaber's Theorem on Power Sum at arxiv, he actually managed to formulate for odd power. #4 20120721 02:31:57
Re: A Development of New Numerical Analysis MethodHi; A first, crude bound on the sum is 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 20120722 11:45:00
Re: A Development of New Numerical Analysis MethodThanks for the formula bobbym! Using mathcad, you would get the value of . Using method of area integration, , where "a" is the first term and "b" the final term . My method is simple and giving better accuracy. I would write it down later on.Last edited by Stangerzv (20120722 11:46:04) #6 20120722 13:43:37
Re: A Development of New Numerical Analysis MethodHi Stangerzv; 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. 