How to get the expression of a special function? Like gamma function:
Gamma[z]=Integrate[t^(z-1)/e^t, {t, 0, Infinity}]
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1 Answer
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reps = Entity["MathematicalFunction", "Gamma"][
"IntegralRepresentations"]
reps[[2]][z]
EDIT: Activating all except Integrate
Activate[reps[[2]][z], Except[Integrate]]
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}]
In this case, the most useful available properties are the RelatedFunctions and Wolfram Functions Site link
answered Feb 1, 2022 at 2:56
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$\begingroup$ Thank you very much! @Bob Hanlon $\endgroup$ Commented Feb 1, 2022 at 3:01
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$\begingroup$ 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. $\endgroup$ Commented Mar 15, 2022 at 11:32
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$\begingroup$ OK, thank you very much for your help! $\endgroup$ Commented Mar 16, 2022 at 2:55