5
$\begingroup$

How to get the expression of a special function? Like gamma function:

 Gamma[z]=Integrate[t^(z-1)/e^t, {t, 0, Infinity}]
$\endgroup$
0

1 Answer 1

14
$\begingroup$
reps = Entity["MathematicalFunction", "Gamma"][
  "IntegralRepresentations"]

enter image description here

reps[[2]][z]

enter image description here

EDIT: Activating all except Integrate

Activate[reps[[2]][z], Except[Integrate]]

enter image description here

EDIT: For some functions, many of the properties may be missing. For example, for Hypergeometric2F1

properties = Select[
   Entity["MathematicalFunction"]["Properties"],
   FreeQ[
     Entity["MathematicalFunction", "Hypergeometric2F1"][#],
     Missing] &];

Length /@ {Entity["MathematicalFunction"]["Properties"], properties}

(* {54, 7} *)

Manipulate[
   Entity["MathematicalFunction", 
       "Hypergeometric2F1"][prop], 
   {{prop, EntityProperty["MathematicalFunction", 
         "WolframFunctionsSiteLink"], "properties"}, 
     properties}]

enter image description here

In this case, the most useful available properties are the RelatedFunctions and Wolfram Functions Site link

$\endgroup$
4
  • $\begingroup$ Thank you very much! @Bob Hanlon $\endgroup$
    – lotus2019
    Feb 1 at 3:01
  • $\begingroup$ Hello, could you tell me how to express the function Hypergeometric2F1? I don't know which code to use for Hypergeometric2F1, such as "IntegralRepresentations" for Gamma. $\endgroup$
    – lotus2019
    Mar 15 at 11:32
  • $\begingroup$ @lotus2019 - see edit. $\endgroup$
    – Bob Hanlon
    Mar 15 at 16:09
  • $\begingroup$ OK, thank you very much for your help! $\endgroup$
    – lotus2019
    Mar 16 at 2:55

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.