Re: why Sqrt[z^2] in Mathematica's web site formulas?
- From: rjf <fateman@xxxxxxxxx>
- Date: Wed, 15 Aug 2007 12:53:47 -0700
On Aug 15, 10:15 am, sashap <pav...@xxxxxxxxx> wrote:
Because
...snip...
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
Thanks for your response.
I object to the unnecessary use of Sqrt (or other fractional powers)
in formulas because there are, especially in the complex plane,
multiple possible values for associated mathematical notion of square
root. To use such symbolic representations SYMBOLICALLY, when the
argument to Sqrt is not a particular constant, but is a formula like
z^2, subject to other manipulations or simplifications, is often
asking for trouble.
In this formula there is an issue of mapping a complex number to
another complex number. The (single-valued, i.e. true) functions Arg
and Abs are available. I think that the two items in the list below
are equivalent in Mathematica, but the second is mathematically
unambiguous: it does not rely on a human or a computer program
choosing a branch of the square root.
cc = {Sqrt[z^2], Exp[ Mod[Arg[z], Pi/2]*I]*Abs[z]}
.
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