SELECT 'Müller' = 'Mueller'; do not return 1

[Timothy Chan]

I believe this has been discussed in the past but there has never been any real solution to it. I am trying to simulate the example below:

mysql> SELECT 'Müller' = 'Mueller';
+----------------------+
| 'Müller' = 'Mueller' |
+----------------------+
| 0 |
+----------------------+

mysql> SET collation_connection = latin1_german2_ci;

mysql> SELECT 'Müller' = 'Mueller';
+----------------------+
| 'Müller' = 'Mueller' |
+----------------------+
| 1 |
+----------------------+

But I am not getting as it supposed to although I have set the collation to latin1_german2_ci.

When I do a hex, I get the following:

mysql> select hex('Müller');
+---------------+
| hex('Müller') |
+---------------+
| 4D816C6C6572 |
+---------------+

mysql> select hex('Mueller');
+----------------+
| hex('Mueller') |
+----------------+
| 4D75656C6C6572 |
+----------------+

Any guru out there please help.

Thank you.