2002 II 3
From QED
The equation is:
If we write , then we can take the derivative to find the saddles:
Which can be simplified for large x and t from 0 to 1 to be approximately:
Then the only saddle is at t = π / 6. The second derivitive is:
So the direction is , so it is real (for positive real x), and we can integrate through it. Doing this, we get:
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