Re: ProductLog[-Pi/2]

• To: mathgroup at smc.vnet.net
• Subject: [mg44182] Re: ProductLog[-Pi/2]
• From: "Christos Argyropoulos M.D." <argchris at otenet.gr>
• Date: Sat, 25 Oct 2003 06:26:35 -0400 (EDT)
• References: <bnapg7\$4lk\$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```Hi,
Actually this is the expected behaviour;
You entered an exact number in the ProductLog function, and you get back an
exact number (i.e. ProductLog[Pi/2])
Mathematica will keep this special function result in this exact format,
unless requested to return a numeric result.
Try ProductLog[1], will return the same thing.
If getting back I Pi/2 is crucial to your application try the following:

In[1]:=
ProductLog[-Pi/2]
ProductLog[N[-Pi/2]]//Chop
Unprotect[ProductLog];
ProductLog[-Pi/2]= I Pi/2;
Protect[ProductLog];
ProductLog[-Pi/2]

Out[1]=
\!\(ProductLog[\(-\(\[Pi]\/2\)\)]\)
Out[2]=
1.5708 \[ImaginaryI]
Out[6]=
\!\(\(\[ImaginaryI]\ \[Pi]\)\/2\)

Best Regards
Christos Argyropoulos MD
Athens, Greece

----- Original Message -----
To: mathgroup at smc.vnet.net
Subject: [mg44182] ProductLog[-Pi/2]

> ProductLog[-Pi/2] should return I Pi/2 but doesn't...
>
> In[1] := w E^w /. w -> I Pi/2
> Out[1] = -Pi/2
>
> In[2] := ProductLog[-Pi/2] // FullSimplify
> Out[2] = ProductLog[-Pi/2]
>
> In[3] := ProductLog[-Pi/2] // N // Chop
> Out[3] = 1.5708 I
>
> Could someone explain ? (I use Mathematica 4.1)
>
> ---
> jcp
>

```

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