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Two Roads

tworoads

This post is homage to the amazing power of approximation of asymptotics. A finite number of terms of a divergent series can rapidly approach the value of a function while a convergent series needs an extremely large number of terms to get to the same accuracy and precision.

1/\Gamma (x) is the illustrative function (chosen as  mentioned in Professor Bender lecture on Mathematical Physics). The plot shows the single term Stirling approximation/function (obviously begs the question what algorithm does Mathematica used) v partial sums of power series/function.

 

asymptotic

 

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Categories: Mathematica, Mathematics
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