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Series acting on a symbolic function

  • To: mathgroup at smc.vnet.net
  • Subject: [mg109494] Series acting on a symbolic function
  • From: Igor Khavkine <igor.kh at gmail.com>
  • Date: Fri, 30 Apr 2010 05:49:31 -0400 (EDT)

I would like to define a custom special function in Mathematica, let
me call it F[x]. I want it to behave like Sin[x], BesselJ[0,x], etc.
If the argument is symbolic, I do not want Mathematica to do any
special simplifications or evaluations. However, when using Series[]
in an expression like

  Series[... F[x] ..., {x,...}]

I want Mathematica to be able to expand F[x] about any particular
point, keeping in mind that F[x] is not analytic everywhere and may
have special branch points about which a Puiseux or Log/power series
expansion must be used.

What is the standard way of defining such behavior on F[x]?

Thanks in advance.

Igor


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