If you look at the implementations you'll see that many of the functions 
have derivatives, arbitrary precision complex numerical evaluation, some 
simplification for specific input, and an interface to Maxima for integrals 
and other simplifications. The linked patches address these issues for 
functions that don't have them.

On Tuesday, 10 September 2013 17:24:42 UTC-7, rjf wrote:
>
>
>
> On Tuesday, September 10, 2013 1:36:02 PM UTC-7, Eviatar wrote:
>>
>> Hello,
>>
>> I made a table of the status of special functions in 
>> Sage<http://www.phas.ubc.ca/~eviatarb/?e=11>, 
>> based on the one in the Digital Library of Mathematical Functions. I 
>> thought it would be of interest to some people here. It also links to 
>> pending patches implementing or making improvements to functions in Sage.
>>
>> Eviatar
>>
>
> It is kind of naive, in a discussion relevant to Sage, to talk about 
> mathematical functions being
> "implemented"  as a checklist.  Compare DLMF to (say) the Wolfram 
> functions web site.
>
> When you say F is "implemented", does that mean numerical evaluation for
> double-precision float arguments?  How about arbitrary precision?  How 
> about
> integration of F(x) and expressions involving it?   How about derivatives?
> How about addition formulas  and relations with other functions?
>
> Its sort of like comparing geographical locations and having a checklist:
>
>                      US      France  Italy   Antarctica
> red wine         x          x            x       0
> white wine      x          x            x       0
>         
>

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