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.

1. Missing a Rationale
2. Should the m argument on the Associated Laguerre, Associated Legendre, and Spherical Legendre be implementation-defined for values >= 128?
3. Specify a macro that would hide the new functions — something along the lines of __STDC_WANT_MATH_SPEC_FUNCS__.
4. Should there be a reference to J in 2.1.10 and 2.1.19?
   Note: J is defined in 2.1.8.
5. Should there be a reference to N in 2.1.21?
   Note: N is defined in 2.1.10.
6. Should Jerome Spanier and Keith B. Oldham: An Atlas of Functions, Hemispere Publishing Corp, 1987 be added to the Bibliography?
7. 2.1.2 associated Legendre functions, should (-1)**M be added to definition?
8. 2.1.2 associated Legendre functions, should for odd M then |x|<=1 be added?
9. 2.1.3 beta function, what happens when X and/or Y is a zero or negative integer?
10. 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
11. 2.1.4 (complete) elliptic integral of the first kind, should 0<=k<=1 be added?
12. 2.1.4 (complete) elliptic integral of the first kind, should K(1.) is +INF be added?
13. 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?.
14. 2.1.5 (complete) elliptic integral of the second kind, should 0<=k<=1 be added?
15. 2.1.5 (complete) elliptic integral of the second kind, should E(1.) is +1.
16. 2.1.6 (complete) elliptic integral of the third kind, should effects use k and nu?
17. 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.
18. 2.1.6 (complete) elliptic integral of the third kind, should it be PI(nu,k) instead of PI(nu,k,pi/2)?
19. 2.1.6 (complete) elliptic integral of the third kind, should |k| <= 1 be added?
20. 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?
21. 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.
22. 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?
23. 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?
24. 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?
25. 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.
    ?
26. 2.1.8 cylindrical Bessel functions (of the first kind), should (x/2)**nu before the summation sign in the math formula be removed?
27. 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?
28. 2.1.9 irregular modified cylindrical Bessel functions, should K(0.) is +INF be added?
29. 2.1.13 (incomplete) elliptic integral of the third kind, should the formula in the denomerator be changed to (1 + nu*sin(phi)**2)?
30. 2.1.13 (incomplete) elliptic integral of the third kind, should the arguments be reorder to nu, k, phi to match the math function?
31. 2.1.14 exponential integral, should the formula be changed from Ei(-INF) = integral from -INF to x of exp(t)dt/t?
32. 2.1.14 exponential integral, should the following be added Ei(-INF) is 0, Ei(0) is -INF, Ei(+INF) is +INF?
33. 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);

    ?
34. 2.1.17 Legendre polynomials, why |x| <= 1? Functions are defined for all x.
35. 2.1.18 Riemann zeta function, zeta(0.5) does not match the Handbook of Mathematical Function.
36. 2.1.18 Riemann zeta function, should zeta(1.) is +INF be added?