**Document:** WG14 N1185

**Date:** 2006/08/04

**Author:** Benito

**Subject:** Open issues from Registration
Review of TR 24747

The intention of this document is to list the issues that were not included in the N1182 document that was forwarded to SC22 for registration ballot but mentioned by one or more of the reviewers. The list is in no particular order.

- Missing a Rationale
- Should the
`m`

argument on the**Associated Laguerre**,**Associated Legendre**, and**Spherical Legendre**be implementation-defined for values`>= 128`

? - Specify a macro that would hide the new functions —
something along the lines of
`__STDC_WANT_MATH_SPEC_FUNCS__`

. - Should there be a reference to

in 2.1.10 and 2.1.19?**J**

**Note:**

is defined in 2.1.8.**J** - Should there be a reference to

in 2.1.21?**N**

**Note:**

is defined in 2.1.10.**N** - Should Jerome Spanier and Keith B. Oldham:
*An Atlas of Functions*, Hemispere Publishing Corp, 1987 be added to the Bibliography? - 2.1.2
*associated Legendre functions*, should`(-1)**M`

be added to definition? - 2.1.2
*associated Legendre functions*, should for odd`M`

then`|x|<=1`

be added? - 2.1.3
*beta function*, what happens when`X`

and/or`Y`

is a zero or negative integer? - 2.1.3
*beta function*, should the following text be added?

`B(x,-x) is ((-1)**x)/x)`

when`x`

is an integer, and is`0`

when`x`

is not an integer - 2.1.4
*(complete) elliptic integral of the first kind*, should`0<=k<=1`

be added? - 2.1.4
*(complete) elliptic integral of the first kind*, should`K(1.)`

is`+INF`

be added? - 2.1.5
*(complete) elliptic integral of the second kind*, in*Atlas of Functions*has`E(k)`

not`E(k,pi/2)`

.

**Note:**This document is not based on*Atlas of Functions*, C++ compatibility?. - 2.1.5
*(complete) elliptic integral of the second kind*, should`0<=k<=1`

be added? - 2.1.5
*(complete) elliptic integral of the second kind*, should`E(1.)`

is`+1`

. - 2.1.6
*(complete) elliptic integral of the third kind*, should**effects**use`k`

and`nu`

? - 2.1.6
*(complete) elliptic integral of the third kind*,*Atlas of Functions*has`(1+nu*sin(theta)**2)`

in denominator; not`(1-nu*sin(theta)**2)`

.

**Note:**See note bullet 13. - 2.1.6
*(complete) elliptic integral of the third kind*, should it be`PI(nu,k)`

instead of`PI(nu,k,pi/2)`

? - 2.1.6
*(complete) elliptic integral of the third kind*, should`|k| <= 1`

be added? - 2.1.6
*(complete) elliptic integral of the third kind*, should`PI(nu,1.)`

is`sign(nu)*INF`

;`PI(-1,k)`

is`INF`

*not sure of its sign*be added? - 2.1.6
*(complete) elliptic integral of the third kind*, Why is C function`f(k,nu)`

, while math function is`f(nu,k)`

? Seems like the C function argument order should be swapped. - 2.1.7
*regular modified cylindrical Bessel functions*, should the note

This function is also known as Hyperbolic Bessel function and modified Bessel function of the first kind be added? - 2.1.7
*regular modified cylindrical Bessel functions*, should the text

If`nu`

is an integer, then the function is defined for all real`x`

.**Note:**In fact, they are even/odd functions if`nu`

is even/odd.

be added? - 2.1.8
*cylindrical Bessel functions (of the first kind)*, should the text

`gamma(nu+k+1)`

is`(nu+k)!`

when`nu`

is an integer

be added? - 2.1.8
*cylindrical Bessel functions (of the first kind)*, should

for`x>=0`

be replaced with

for all`x`

when`nu`

is an integer,for`x>=0`

when`nu`

is not an integer.

? - 2.1.8
*cylindrical Bessel functions (of the first kind)*, should`(x/2)**nu`

before the summation sign in the math formula be removed? - 2.1.9
*irregular modified cylindrical Bessel functions*, should the note

This function is also known as the Basset function, modified Bessel function of the third kind, MacDonals function, and the modified Hankel function.

be added? - 2.1.9
*irregular modified cylindrical Bessel functions*, should`K(0.)`

is`+INF`

be added? - 2.1.13
*(incomplete) elliptic integral of the third kind*, should the formula in the denomerator be changed to`(1 + nu*sin(phi)**2)`

? - 2.1.13
*(incomplete) elliptic integral of the third kind*, should the arguments be reorder to`nu`

,`k`

,`phi`

to match the math function? - 2.1.14
*exponential integral*, should the formula be changed from`Ei(-INF) = integral`

from`-INF`

to`x of exp(t)dt/t`

? - 2.1.14
*exponential integral*, should the following be added`Ei(-INF)`

is`0`

,`Ei(0)`

is`-INF`

,`Ei(+INF)`

is`+INF`

? -
2.1.15
*Hermite polynomials*, should following be added- —
`H(0,x) = 1;`

- —
`H(1,x) = 2x;`

- —
`H(n,x) = 2xH(n-1,x) - 2(n-1)H(n-2,x);`

- —
- 2.1.17
*Legendre polynomials*, why`|x| <= 1`

? Functions are defined for all`x`

. - 2.1.18
*Riemann zeta function*,`zeta(0.5)`

does not match the*Handbook of Mathematical Function*. - 2.1.18
*Riemann zeta function*, should`zeta(1.)`

is`+INF`

be added?