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Instantuse addon functions for the Wolfram Language
Function Repository Resource:
Find a numerical approximation of a series expansion of a function
ResourceFunction["NSeries"][f,{x,x_{0},n}] gives a numerical approximation to the series expansion of f about the point x=x_{0} including the terms (xx_{0})^{n} through (xx_{0})^{n}. 
This is a power series for the exponential function around x=0:
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Chop is needed to eliminate spurious residuals:
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Using extended precision may also eliminate spurious imaginaries:
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Find expansions in the complex plane:
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Find Laurent expansions about essential singularities:
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Series will not find Laurent expansions about essential singularities:
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Use "Radius" to pick the annulus within which the Laurent series will converge:
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Laurent series for x≥3:
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Changing "Radius" can improve accuracy:
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A function defined only for numerical input:
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Find a series expansion of f:
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Check:
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NResidue can also be used to construct a series of a numerical function:
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Using NResidue:
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NSeries can have aliasing problems due to InverseFourier:
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The correct expansion is analytic at the origin:
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SeriesData cannot correctly represent a Laurent series. Here is the square of the series of Exp:
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Here is the SeriesData representation of the Laurent series of Exp:
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Find the series expansion of the generating function for unrestricted partitions:
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Check:
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Wolfram Language 11.3 (March 2018) or above
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