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    power series development


    Hallo

    I have got a mathematical problem.
    I want to approximate an exponential function with a taylor polynom.

    1+x+x^2/2+x^3/6+...+x^n/n!+....

    Depending on the intervall of my value x i need to have a certain amount of polynoms for my approximation. I have found a table with a degree of polynoms that correspond with a specific intervall of x. With this table it is possible to obtain an exponential approximation of 10 digits behind the komma....

    x degree of Polynom
    0.05 5
    0.1 6
    0.2 8
    0.5 10
    1 13
    2 17
    5 25
    10 36

    The question i have is not mathematically easy to solve.
    Can somebody show me the mathematical derivation of this table ?

    Thank you !!!
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    i would imagine the table was derived by calculating terms of the taylor series / maclaurin series until the (total of the outstanding) terms become insignificant.

    on the other hand there may be a direct calculation of the remainder series (ie the terms from n+1 to infinity) that if you need a proper mathematical derivation.

    for what it's worth i make the last two 28 and 43 in excel (not 25 and 36)

    edit:- i think your table is accurate to ten significant digits rather than ten digits after the comma as you say.
    Last edited by epl; August 22nd, 2003 at 04:28 PM.

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