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Full Version: Lambert W functions on WP 34s
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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,

FYI, W^-1 represents the inverse of W in the WP 34S.

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.

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
```

Edited: 25 Nov 2011, 10:54 a.m.

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.

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

Pauli, [sub-1] ??

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

Exactly. And we feature [sub-m] and [sub-p] ... :-)

I know that was why I mentioned them ;-)

- Pauli

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.

Great!