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I'm trying to get mathematicas series function to output a result that look like this:

enter image description here

instead of calculating the actual "values", like doing so here:

seriesfunc = Sin[x] Cos[x]/x
(* (Cos[x] Sin[x])/x *)

Series[seriesfunc, {x, 0, 5}]
(* 1-(2 x^2)/3+(2 x^4)/15+O[x]^6 *)

Is this possible? Yes, it is part of homework (or Calculus II exam actually), but I still think it's allowed here.

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2 Answers 2

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I think SeriesCoefficient is what you want. Then you can use it to display formatted formulas

 series[expr_, x_, x0_] := Defer[expr = Sum[#, {n, 0, ∞}]] &[
  FullSimplify@SeriesCoefficient[expr, {x, x0, n}, Assumptions -> {n >= 0}] (x - x0)^n]

series[Sin[x] Cos[x]/x, x, 0]

enter image description here

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    $\begingroup$ You may want it elegantly typed, wrap TeXForm around the result and paste the results into a TeX word-processing system. $\endgroup$
    – David G. Stork
    Commented Jan 12, 2015 at 23:59
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If you hit = in a clean cell twice the cell will turn into a Wolfram Alpha cell, and you can ask it using the English language. It will give you the series expansion as well as a series representation:

Taylor approximation through Wolfram Alpha

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