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You are not logged in. #1 20131110 09:58:01
Infinite series helpHello. will be of the form such that if computed will yield the desired function. I have confirmed this in Maple. How do I go about doing this by hand so as to show all my work? Computing it in Maple is easy but I want to know how to do it for myself. I attempted the problem myself, treating it as an integration problem but that didn't work and it makes sense that it didn't work because I am counting to infinity instead of finding the area under a curve. Any help is appreciated. #2 20131110 10:35:33
Re: Infinite series helpHi; 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 20131111 06:32:21
Re: Infinite series helpHi; It is easy to demonstrate the work to produce such a 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. #5 20131111 07:59:31
Re: Infinite series helpI see what you are saying and I already know that. When it is around zero it is a Maclaurin series. My original question is, how do I go from to without the aid of a computer program like Maple? Is there a way to compute it by hand like an integral? That is the information I am lacking. #6 20131111 08:29:08
Re: Infinite series helpIt is easy to go from the function to the series but to go back might not be as easy since I have never seen it done. If you were to undo the differentiations that still would not produce the original function just another polynomial. Now it is obvious that no matter what we do to that we will never get sin(x) back. 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 20131111 17:46:43
Re: Infinite series helpHi; Yes, they are the same thing for certain values only. Sometimes when you see the series on the right you are able to recognize which function it belongs to. In most cases you will not. You could always curve fit but you must again already know the form on the left.
The Taylor series is very useful in numerical work. It is used to approximate functions and to develop new methods 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 20131112 01:50:03
Re: Infinite series helpHi; 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 20131112 01:56:55
Re: Infinite series helpTo remember that might be useful if you could get the sum in analytical form for an upper bound of n. Then you could use the laws of limits to get the sum to infinity. This is only theoretical as far as I am concerned. It is almost never easier to get the sum to n rather than infinity. 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 20131112 20:45:35
Re: Infinite series help
We can form a second order differential equation and get it from there. 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 #14 20131113 10:01:38
Re: Infinite series help
How? or or or something else? They can all be interpreted to mean the same thing but I do not know if any of them are better than the rest. #15 20131113 10:14:16
Re: Infinite series helpHi; 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. 