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Series Expansions in Mathematica

  • To: mathgroup at
  • Subject: [mg129871] Series Expansions in Mathematica
  • From: Samuel Mark Young <sy81 at>
  • Date: Tue, 19 Feb 2013 18:53:54 -0500 (EST)
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I am attempting to expand an equation, and then solve the 1st, 2nd, 3rd, 4th and 5th order expressions one at a time.

The equation is:

Exp[4 x] - c Exp[3 y] Exp[4 x] + c - 1 = 0

With, x and y small variables to be expanded and c a constant. Once this is expanded, the variables x and y are in turn replaced with expansions written as:

x = x[1] + x[2]/2 + x[3]/6 + x[4]/24 + x[5]/120 (to 5th order)

By the time I have completed these expansions, I have a somewhat long expression. Does Mathematica have an intelligent way of deciding which terms would be 1st/2nd/etc order? For example, x[1] y[2] and x[1]^2 y[1] would both be third order.

Many thanks,
Sam Young

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