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Series bug for ParabolicCylinderD ?

Posted 10 years ago

Series gives two different results at the leading $Sqrt[1/x]$ term... The second is the correct one. enter image description here

POSTED BY: Aharon Davidson
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Posted 10 years ago

Thanks for the reply,

Of course things look less dramatic when you know the correct result, and then you can find ways around, but we were that close to publish a paper which includes a garbage result... It is a bug! The first result is wrong in three respects:

  1. No O(1) corrections.

  2. Half of the O(x^{-1/2}) term is missing.

  3. While O(x^{-1}) is present, no O(x^{-1/2}) corrections are mentioned.

POSTED BY: Aharon Davidson

Find Series[x^(1/2)D] then multiply by x^(-1/2):

In[1]:= Series[
 x^(1/2) ParabolicCylinderD[-(1/2), (-1 + I) x], {x, \[Infinity], 0}]

In[2]:= Series[
 x^(1/2) ParabolicCylinderD[-(1/2), (-1 + I) x], {x, \[Infinity], 1}]

You get same result for both inputs.

POSTED BY: S M Blinder
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