HP Forum Archive 20

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Lambert W functions on WP 34s Message #1 Posted by Hans Milton on 25 Nov 2011, 9:00 a.m. It is impressive to see the Lambert W functions included in WP 34s. However, the W-1 function give incorrect results. Example: x ex = -0.2 has two solutions -0.259171 -2.542641 On the emulator W(-0.2) correctly returns the first solution. But W-1(-0.2), which is expected to give the second solution, instead returns -0.163746

Re: Lambert W functions on WP 34s Message #2 Posted by Walter B on 25 Nov 2011, 9:26 a.m., in response to message #1 by Hans Milton FYI, W^-1 represents the inverse of W in the WP 34S.

Re: Lambert W functions on WP 34s Message #3 Posted by Hans Milton on 25 Nov 2011, 10:10 a.m., in response to message #2 by Walter B I see. What I thought was the Lambert W-1 function is actually the inverse of the Lambert W0 function. Which could also be easily calculated as x ex. W-1 is not so easily calculated. So would be more useful to have on the calc.

Re: Lambert W functions on WP 34s Message #4 Posted by Walter B on 26 Nov 2011, 4:57 a.m., in response to message #3 by Hans Milton With the next software build, you'll find both branches on the WP 34S: Wp for the principal branch and Wm=W-1 for the lower branch. The latter is calculated by an XROM routine, so it may not be as accurate as Wp.

Re: Lambert W functions on WP 34s Message #5 Posted by Hans Milton on 26 Nov 2011, 8:14 a.m., in response to message #4 by Walter B Great!

Re: Lambert W functions on WP 34s Message #6 Posted by Gerson W. Barbosa on 25 Nov 2011, 10:15 a.m., in response to message #1 by Hans Milton Easily done on the HP-12C: 01 CHS 02 1/x 03 STO 0 04 STO 1 05 LN 06 RCL 0 07 * 08 RCL 1 09 x<>y 10 - 11 x=0 12 GTO 15 13 LST x 14 GTO 04 15 LST x 16 RCL 0 17 / 18 CHS 19 GTO 00 -0.2 R/S -> -2.542641358 http://www.hpmuseum.org/cgi-sys/cgiwrap/hpmuseum/archv019.cgi?read=159032 Edited: 25 Nov 2011, 10:54 a.m.

Re: Lambert W functions on WP 34s Message #7 Posted by Paul Dale on 25 Nov 2011, 6:52 p.m., in response to message #6 by Gerson W. Barbosa It would be easy enough to include a user code programme to calculate this branch of the W function in the device -- for real arguments only. I'd guess 100 or so bytes of precious flash. Alternatively, use this program: 01 LBL'W[sub-1]' 02 LocR 02 03 STO .02 04 +/- 05 1/x 06 STO .00 07 STO .01 08 LN 09 RCL[times] .00 10 RCL .01 11 x[<->] Y 12 - 13 x=0? 14 SKIP 03 15 DROP 16 RCL L 17 BACK 10 18 DROP 19 RCL L 20 RCL/ .00 21 +/- 22 x[<->] .02 23 STO L 24 x[<->] .02 25 RTN Store it in one of the flash segments and you've got the W-1 function. It behaves like a keyboard command in that Last X is set properly and the stack is not damaged. The argument range is not correctly validated however. - Pauli

Re: Lambert W functions on WP 34s Message #8 Posted by Walter B on 25 Nov 2011, 6:59 p.m., in response to message #7 by Paul Dale Pauli, [sub-1] ??

Re: Lambert W functions on WP 34s Message #9 Posted by Paul Dale on 25 Nov 2011, 7:30 p.m., in response to message #8 by Walter B Yeah, [sub-1] which displays as 1. We don't have a subscript minus or minus 1. All our codes for subscripts are [sub-X]. The other convention I've seen is Wm and Wp for w-1 and W0 respectively. - Pauli

Re: Lambert W functions on WP 34s Message #10 Posted by Walter B on 26 Nov 2011, 3:20 a.m., in response to message #9 by Paul Dale Exactly. And we feature [sub-m] and [sub-p] ... :-)

Re: Lambert W functions on WP 34s Message #11 Posted by Paul Dale on 26 Nov 2011, 3:27 a.m., in response to message #10 by Walter B I know that was why I mentioned them ;-) - Pauli

Re: Lambert W functions on WP 34s Message #12 Posted by Ángel Martin on 25 Nov 2011, 10:49 a.m., in response to message #1 by Hans Milton Just in case it's useful, functions WL1 and WL0 are available in the SandMath-II module for the HP-41, both implemented in MCODE. The module is available at TOS for V41 and i41CX usage - also possible to burn into Clonix, MLDL2k, etc. of course. Cheers, ÁM Edited: 25 Nov 2011, 10:49 a.m.

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