| Title: | Mathematics at DEC |
| Moderator: | RUSURE::EDP |
| Created: | Mon Feb 03 1986 |
| Last Modified: | Fri Jun 06 1997 |
| Last Successful Update: | Fri Jun 06 1997 |
| Number of topics: | 2083 |
| Total number of notes: | 14613 |
I've lost my book of formulae. While I hunt for it, and in case it doesn't have what I want: - Does anybody have a product form for the arc cosine function: ACOS(X) = A1(X) * A2(X) * A3(X) * ... - How about ACOS(A + B) in terms of functions of A and B alone? - Does the constant 1.302964 look familiar to anybody? John
| T.R | Title | User | Personal Name | Date | Lines |
|---|---|---|---|---|---|
| 417.1 | TOOLS::STAN | Wed Jan 01 1986 16:31 | 7 | ||
I have never seen a formula for ACOS(X+Y). I don't recognize the constant 1.302964. The continued fraction expansion is 1, 3, 3, 3, 13, 1, 1, 4, 1, 6, 3, 2, ... in which I see no pattern. A good rational approximation is 140539/107861. | |||||
| 417.2 | 6263::JANZEN | Thu Jan 02 1986 08:35 | 11 | ||
I'm not sure if this helps, but
Arcos x = pi/2 - Arctan(x/(SQRT(1-x**2)))
CRC Standard Math Tables 18th edition
and the Taylor expansion for Arctan x is:
arc tan x = x-(x**3)/3 + (x**5)/5 - (x**7)/7 + . . . for -1 <=x<=1
page 555 Calculus one and several variables Salas and Hille
so you can get there from here.
Tom
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| 417.3 | 6263::JANZEN | Thu Jan 02 1986 08:46 | 7 | ||
Here's a bettern series arcos = pi/2 - (x+ x**3/2*3 + 1*3*x**5/2*4*5 + 1*3*5*x**7/2*4*6*7+...) x**2<1, 0 < arccos x < pi Tom | |||||