## 2540 Reputation

4 years, 356 days

## is(EllipticK(1) = infinity)...

Maple 2022

I came across this question while trying to verify the equality of expressions containing elliptic integrals.

That's what Maple returns for

However

 (1)

 (2)

indicate infinity.

 (3)

 (4)

I have no experience with elliptic integrals. Can I assume in this case that infinity is correct?

## Why does Maple not simplify to infinity?...

Maple

Evaluating this integral

 (1)

 (2)

produces an infinite product as output. Why does Maple not automatically simplify to infinity. Can the extra information (1+pi) be of any use?

## Why is simplify ineffective with these c...

Maple

The expression

 (1)

simplifies to zero in the real range if y=0 is excluded.

 (2)

 (3)

Combining the above assumptions as attempted bellow does not simplify to zero

 (4)

 (5)

 (6)

 (7)

 (8)

## is(-arctan(-x, y) = arctan(x, y))?...

Maple

In the positive range Maple confirms that this is true.
In the real range Maple fails to provide an answer (see attachments).

Is this identity correct?

 (1)

 (2)

 (3)

 (4)

 (5)

But

On a unit circle

 (6)

 (7)

 (8)

 (9)

 (10)

and another maybe related case where simplification does not work

arctan_xy_simplify_2.mw

## Solve & Trig: Why is the output differen...

Maple

Solve produces different output in the attachment depending on how it is used. Why is that and how can simplification to arctan(y/z) be avoided? Arctan(y/z) only gives correct angles for positive y and z.  I prefer arctan(y,z) output that I can subsequently simplify to the y and z ranges of interest (if possible). Imagine “wrong” simplification of complex algebraic output (e.g., from inverse kinematics).

Arctan.mw

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