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A question on infinities .

  1. Mar 1, 2005 #1
    A question on infinities.....

    we all know that the function [tex]e^{-x^2}[/tex] can be expanded into a taylor series my question arises when we try to perform the integral:


    then if we expand exp(-x^2) in terms of its Taylor series and perform the integration we would find that:


    the question is if a sum of infinities can give a finite number such as happens in the last sum... where the a_n are the taylor coefficients of the series expansion for exp(-x^2)
    Last edited: Mar 1, 2005
  2. jcsd
  3. Mar 1, 2005 #2

    matt grime

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    The sum makes no sense: you're not even adding up real numbers. At least take limits first, and then ask if it is permissible to interchange limits and summation signs. (answer, not always - this is basic analysis, not number theory.)
  4. Mar 1, 2005 #3


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    To evaluate the integral, the simplest approach that works is first square it, then change the variables in the double integral to polar coordinates. You will then very easily get pi/4 for the squared integral.
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