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?