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The answer will depend on the nature of the differential equation.
The numerical value of pi is often found using a Taylor or Maclaurin series (Taylor series centered at 0).
f(x)=lnx
A power series in mathematics (in one variable) is an infinite series of a certain form. It normally appears as the Taylor series of a known function.
A data series is a collection of data, most likely numbers, that you would use to graph or solve an equation.