While trying to find the circumference of an ellipse, I came up with this result in Wolfram Alpha.
Equation: $\dfrac{x^2}{a^2} + \dfrac{y^2}{b^2} =1$
While trying to perform the definite integral, the computation timed out.
2026-03-27 11:45:13.1774611913
What does the function $E$ stand for in WolframAlpha's solution to this integral?
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Wolfram Alpha usually specifies things like these below the equation and to the right, often linking to properties and definitions. Indeed, putting your integral into Wolfram Alpha:
The function $E$, here, refers to elliptic integrals of the second kind.
The site also links to its definition and a page on its properties and such.
Sadly, all this is way above my head, so in parsing said information I will likely be of absolutely no help to you. Good luck though!