@W-E-Brown This looks correct to me; what do you think?

[Walter says some correspondence has got lost here. I'll try to chase up @apolukhin in person.]

On Nov 9, 2016, at 1:04 PM, Thomas Köppe notifications@github.com wrote:

[Walter says some correspondence has got lost here. I'll try to chase up @apolukhin in person.]

Here's my previous response:

Begin forwarded message:

Subject: Re: [cplusplus/draft] Special math functions editorial issues found by Matwey V. Kornilov f… (#957)
From: W Brown webrown.cpp@gmail.com
Date: 2016-10-25 at 6:40:27 PM CDT
To: cplusplus/draft reply@reply.github.com

On Oct 25, 2016, at 4:20 PM, Richard Smith notifications@github.com wrote:

@W-E-Brown This looks correct to me; what do you think?

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• Clause "Associated Legendre polynomials" is wrongly entitled. "Associated Legendre functions" would be more appropriate here. Though "Associated Legendre polynomials" term is sometimes used it is formally wrong term. A polynomial (by definition) is a particular kind of function which can be represented using only finite number of additions, multiplications and exponentiations to a non-negative power, i.e. in canonical form of SUM(AiX^i). Obviously, some of P^m_l are not polynomials. For instance, for m=l=1, P11(x) == sqrt(1 − x*x) is not representable as SUM(AiX^i). See for reference: Abramowitz and Stegun, Chapter 8 "Legendre Functions".

While I agree in principle, there is another consideration:

When these names were first selected, they were adopted from the equivalent functions mentioned in (what was then) ISO 31, since that document served as our litmus test to answer the question "which special functions should we include?"

ISO 31 has since been updated (Wikipedia says, "ISO/IEC 80000 supersedes both ISO 31 and part of IEC 60027"), and I don't at the moment have access to an updated copy to consult re its current names for these.

If someone can locate a current copy, I recommend we use whichever naming that ISO has adopted therein. In the meantime, I'll look for a copy at our library.

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• "[sf.cmath.cyl_bessel]" is a bad name for the tag. "[sf.cmath.cyl_bessel]" sounds like "Bessel functions" and when people say "Bessel functions" they usually mean Jν from [sf.cmath.cyl_bessel_j]. Replaced "[sf.cmath.cyl_bessel]" with "[sf.cmath.cyl_bessel_i]".

I'm okay with this renaming, assuming there's no reason to maintain consistency with the soon-to-go-away other C++ standard.

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• "[sf.cmath.cyl_bessel_k]" misses references to "[sf.cmath.cyl_bessel_j]" and "[sf.cmath.cyl_neumann]" in the "See also" section. In [sf.cmath.cyl_bessel_j] Jv(x) is defined, in [sf.cmath.cyl_neumann] Nν(x) is defined - both of them are used in the "Returns:" section of the [sf.cmath.cyl_bessel_k].

This also looks fine to me; such cross-references are usually helpful.

@apolukhin checked the wording in ISO-80000-2, and apparently they also changed the term from "associated Legendre polynomial" to "associated Legendre function", so this change does indeed keep us in sync with both ISO and factual reality.

For the record, ISO-80000-2 also uses the correct term "function":