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MathGroup Archive 1996

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Best ("Most Standard") Choice for LegendreType?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg4702] Best ("Most Standard") Choice for LegendreType?
  • From: siegman at ee.stanford.edu (AES)
  • Date: Sat, 31 Aug 1996 03:57:25 -0400
  • Organization: Stanford University
  • Sender: owner-wri-mathgroup at wolfram.com

   I'm writing up an engineering analysis in which the results are
expressed in terms of Legendre polynomials LegendreP[n,m,z] with z real
and >1, that is, outside the more common -1<z<1 range.

   I realize that there are multiple choices used in the literature, and
that in the region of interest to me the only difference is the phase
angle of the answer; but would anyone want to recommend a "preferred
choice" or "most common choice" as between LegendreType->Real or Complex?

   I'm influenced myself by the fact that formula 8.6.16 on page 334 of
Abramowitz and Stegun seems to match up with the Complex and not the Real
type; but are there any counterarguments?  On the other hand Mathematica's
default is Real, not Complex.  Any other arguments either way?

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