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
J
in
2.1.10 and 2.1.19?
Note: J
is defined in 2.1.8.
- Should there be a reference to
N
in
2.1.21?
Note: N
is defined in 2.1.10.
- 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?