# Question:Can Maple help to confirm equality of these elliptic expressions (or the opposite)

## Question:Can Maple help to confirm equality of these elliptic expressions (or the opposite)

Maple

 (1)

(This question has its origin here).
Plotting the difference of rhs - lhs seems to indicate equality over the range [0..1)

Try simplify

 (2)

Try combine

 (3)

Try conversion to integral form

 (4)

 (5)

 (6)

There seems to be a finite difference at

Try an addition theorem from DLMF

Since all elliptic expression have the same modulus k, the following addition theorem could be applied under the condition that the corresponding case is fulfilled https://dlmf.nist.gov/19.11#E7

Check if the following case applies (i.e. is ψ=π/2?)

 (7)

 (8)

 (9)

 (10)

 (11)

 (12)

 (13)

 (14)

lhs and rhs are not equal -> Case  does not apply (provided that the formulas have been applied correctly).
Perhaps this is why Maple does not simply the difference to zero.

Anything else that could be tried in Maple (maybe with other formulas)?