One of the new features in Mathematica 12.
1 is the function Asymptotic.
Here’s a quick example of using it.
Here’s an asymptotic series for the log of the gamma function I wrote about here.
If we ask Mathematica Asymptotic[LogGamma[z], z -> Infinity] we get simply the first term: But we can set the argument SeriesTermGoal to tell it we’d like more terms.
For example Asymptotic[LogGamma[z], z -> Infinity, SeriesTermGoal -> 4] yields This doesn’t contain a term 1/z4, but it doesn’t need to: there is no such term in the asymptotic expansion, so it is giving us the terms up to order 4, it’s just that the coefficient of the 1/z4 term is zero.
If we ask for terms up to order 5 Asymptotic[LogGamma[z], z -> Infinity, SeriesTermGoal -> 5] we do get a term 1/z5, but notice there is no 4th order term.
A note on output forms The Mathematica output displayed above was created by using Export[filename, expression] to save images as SVG files.
The alt text for the images was created using InputForm[expression].
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