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Suppose I have found an irrational number, say e^x upto m decimal places....

Now I want to find upto say m+n decimal places. Is there any way that I can use the previous value of e^x upto m decimal places to help me find the remaining n decimal places? (I can save some number, say, like remainder, when finding upto m decimal places to help me find the later digits...)

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    Possible duplicate: http://math.stackexchange.com/questions/5420/iterative-refinement-algorithm-for-computing-expx-with-arbitrary-precision2011-01-22
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    It probably depends on how you calculated the first $m$ decimal places. If you did it using the series you could just continue adding smaller terms to increase your accuracy.2011-01-22
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    @user3123.. how can I continue adding terms, because the previously computed terms won`t be of the required accuracy...2011-01-22

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