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Solving to the exact

  1. Aug 10, 2010 #1
    Is is possible to solve every real integral and come up with an actual solution? perhaps we may have not just found the methods of doing so. Or is it a must to use approximations(series/sequences) to do so?
    Or is there a way to reverse numerical numbers to come up with a function?
  2. jcsd
  3. Aug 10, 2010 #2


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    It really depends on what you mean by "actual solution".

    Taylor series aren't approximations, by the way. You can truncate the series after a finite number of terms to produce an approximation, but the Taylor series itself is an exact representation of an analytic function -- at least within its radius of convergence.
  4. Aug 10, 2010 #3
    right. I guess all series can be expressed as functions with n to infinite within its convergence.

    So, perhaps the real question is could we establish functions as a non series, or do we need them?
    Last edited: Aug 11, 2010
  5. Aug 11, 2010 #4


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    I think you need to formulate a precise question. What do you mean by "establish functions as a non series"?
  6. Aug 11, 2010 #5
    I think what he means is to define a function analytically without using a series expansion, and I believe the answer you are looking for is that, short of defining a function as the integral of another function(for example, the logarithmic integral function), we currently cannot define some functions short of a series expansion.
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