When I solve for

EllipticF[1.4, 0.9]

with Mathematica or

ellipticF(1.4, 0.9)

with Mupad I get


on both. But when I try

EllipticF(1.4, 0.9)

with Maple, I get some complex number

1.036603009 - 1.654616668*I

The result I need is that which I get with Mathematica and Mupad; how do I get it with Maple?


  • $\begingroup$ If I define the functions like this it is slower than the built in functions, but at least I now get the same results with every program: org.yukterez.net/F,am.png $\endgroup$
    – Yukterez
    Commented Apr 12, 2016 at 5:42

2 Answers 2


Maple and Mathematica use different conventions for the parameters of the elliptic integrals. Maple follows the convention of Gradshteyn and Ryzhik, Mathematica folows Abramowitz and Stegun. Thus Maple's $\text{EllipticF}(x,k)$ is Mathematica's $F(\sin^{-1}(x) \mid k^2)$.

  • $\begingroup$ Thanks, if I define F := (f,k) -> int(1/sqrt(1-k sin(d)^2), d = 0..f) with Maple the result fits. Your answer was as good as the other, but since the other one came first and you already have 200k reputation I'll give the accept to the other guy. Thanks a lot nevertheless! $\endgroup$
    – Yukterez
    Commented Apr 8, 2016 at 1:26

There is a common problem among software libraries that implement special functions: you have to check the definition is the same, and adapt your code accordingly when they are not.

See the definitions for ellipticf in Maple and Mathematica. The arguments are different. In Maple, the first argument is the sine of the amplitude.

For the record, Maxima uses apparently the same definition as Mathematica (I get $2.059$).

See also here on Wikipedia why and how the definitions are different.

  • $\begingroup$ Thanks, now it works, see yukterez.net/forum/viewtopic.php?p=186#p186 $\endgroup$
    – Yukterez
    Commented Apr 8, 2016 at 1:25
  • $\begingroup$ By the way, with the inverse of the function, the Jacobi Amplitude, the second argument must be square rooted with Maple, while with Mathematica and Mupad it goes in straight. $\endgroup$
    – Yukterez
    Commented Apr 8, 2016 at 1:50
  • $\begingroup$ @СимонТыран Yes, it's what Robert Israel wrote in the other answer. I didn't check the details, since I don't have Maple nor Mathematica :-) $\endgroup$ Commented Apr 8, 2016 at 2:00

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