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Is there any command to give me the list of all the embedded elementary functions in Mathematica like Cos Sin Cosh Sinh Log and so on?

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    $\begingroup$ I think you need to define what makes a function elementary. $\endgroup$
    – SPPearce
    Commented Feb 8, 2019 at 12:04
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    $\begingroup$ @kraZug Mathematica has already named it : reference.wolfram.com/language/guide/ElementaryFunctions.html $\endgroup$
    – user49047
    Commented Feb 8, 2019 at 12:08
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    $\begingroup$ I think it is safe to say that if there is an elementary function, then Mathematica has it. Now you get to decide what functions are elementary. $\endgroup$
    – Somos
    Commented Feb 8, 2019 at 18:30

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There doesn't seem to be a direct way to use WolframLanguageData to get only the functions listed on the referenced page of elementary functions. The expression

WolframLanguageData[
 EntityClass[
  "WolframLanguageSymbol", {"FunctionalityArea", "BasicFunctions"}]]

gives rather more than asked for. There doesn't seem to be a functionality area closer to what is wanted.

Never mind, we can always read the documentation and do a little string hacking maybe:

n1 = Import[$InstallationDirectory ~~ "/Documentation/English/System/Guides/ElementaryFunctions.nb", "Text"];

and then after a little data-tasting ...

StringCases[n1, 
 "HelpLookup[\"paclet:ref/" ~~ fn : WordCharacter .. ~~ "\"" :> fn]
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Another way to enumerate the elementary functions would be through MathematicalFunctionData[]:

FromEntity /@ MathematicalFunctionData["ElementaryFunctions"]
   {ArcCos, ArcCosh, ArcCot, ArcCoth, ArcCsc, ArcCsch, ArcSec, ArcSech, ArcSin, ArcSinh,
    ArcTan, ArcTanh, ArcTan[#1, #2] &, Cos, Cosh, Cot, Coth, Csc, Csch, Exp, Haversine,
    Log10, Log2, Log[#1, #2] &, Log, #1^#2 &, ProductLog, ProductLog[#1, #2] &, Sec, Sech,
    Sin, Sinc, Sinh, Sqrt, Tan, Tanh}

Note the separate entries for the one-argument and two-argument versions of Log[], ArcTan[], and ProductLog[].

One might argue that the Lambert function ProductLog[] is not actually elementary, but this is the convention followed by Mathematica. Similarly, one might also wonder why e.g. Gudermannian[], InverseGudermannian[], InverseHaversine[], and LogisticSigmoid[] aren't in the returned list.

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