Re: why Sqrt[z^2] in Mathematica's web site formulas?

Because

In[4]:= {Sqrt[z^2], Abs[z]} /. z -> 1 + I

Out[4]= {1+\[ImaginaryI],Sqrt[2]}


Sqrt[z^2]/z is a constant, in that

In[6]:= D[Sqrt[z^2]/z, z] // Together

Out[6]= 0

which can be +1 or -1, because

In[8]:= (Sqrt[z^2]/z)^2

Out[8]= 1

In BesselJ the presence of such direction dependent constants makes
the asymptotic
expansion formula for Abs[z] -> Infinity valid in all complex
directions.


Oleksandr Pavlyk
Special Functions Developer
Wolfram Research


On Aug 15, 11:28 am, rjf <fate...@xxxxxxxxx> wrote:
Seehttp://functions.wolfram.com/BesselAiryStruveFunctions/BesselJ/06/02/02/
which has asymptotic forms for Bessel functions, includes, repeatedly,
the subexpression Sqrt[z^2].

Any suggestion as to why this would be better than Abs[z]?

RJF


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