Complete Elliptical Integral for the parameters greater than 1 or less than -1

Question

I am trying to compute the Complete elliptical integral of second kind kind in Mathematica with Parameter m=-19.7 .Following is the response from Mathematica.

Input:EllipticE[-19.71] Output:4.81841

I want to know if this is correct or rather how does Mathematica calculate Elliptical integrals for the parameters outside the prescribed range (-1

can you show us your integral? – Dr. Sonnhard Graubner Dec 24 '14 at 13:56 — Dr. Sonnhard Graubner, Dec 24 '14 at 13:56

udit · Answer 1 · 2014-12-24T19:01:30.100

0

I am not sure I understand your question. Why do you think the output you get is wrong?

EllipticE[m] in Mathematica means the following integral -

$$ \int_0^{\pi/2} \sqrt{1-m\sin(t)}dt\,. $$

The integrand is well defined for all $ m $ and so you should expect a proper answer for all m as well. For $ m\le 1 $, this gives a real number (as you got) and for $ m > 1 $, you will get a complex number.

edited Dec 24 '14 at 19:01

answered Dec 24 '14 at 15:29

udit

1

If you have a new question, please ask it by clicking the Ask Question button. Include a link to this question if it helps provide context. – Shaun Dec 24 '14 at 15:49
@Shaun This is not a new question; rather, this is an explanation of some properties of the elliptic integral. – apnorton Dec 24 '14 at 15:51
@anorton Ah, I see. Thank you :) – Shaun Dec 24 '14 at 15:53
I'm sorry about that, @udit – Shaun Dec 24 '14 at 15:53
Thanks Shaun! I guess the initial doubts which I had were due to ambiguity in formulation of elliptical integral from different references. It's resolved now! – Tarun Jan 06 '15 at 09:35

Complete Elliptical Integral for the parameters greater than 1 or less than -1

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