# Question:limit( EllipticF(x*a,r), x=infinity) = ?

## Question:limit( EllipticF(x*a,r), x=infinity) = ?

Maple
```What is limit( EllipticF(x*a,r), x=infinity), a and r complex?

The usual 'limit' returns unevaluated.

'MultiSeries:-limit' gives a result, but it seems to be wrong,
especially for a=I, r=1, but also for other values (no, it is
not a question of Digits):

Tst := [alpha = (-2/(1+2*I*2^(1/2)))^(1/2),
rho = ((1+2*I*2^(1/2))/(1-2*I*2^(1/2)))^(1/2)];

EllipticF(x*alpha,rho);
eval(%,x=2^100): # large value instead of limit
eval(%,Tst):
evalf(%);
1.0010773804561 + 1.4157372084260 I

EllipticF(x*alpha,rho);
MultiSeries:-limit(%, x=infinity);
eval(%,Tst):
evalf(%);
2     1/2
1               (rho  - 1)
-2 EllipticK(---) + EllipticK(-------------) I
rho                   rho
- ----------------------------------------------
rho

-0.34551659067555 - 4.0028945009987 I

Converting to integrals gives another result, which alos can
not be correct.

What is the correct limit? I am missing a proper reference ...
Some of the countless papers of Temme?
```
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