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Past exam of the mathematics course of the University of Cambridge / 2022 / ii / Paper 1 / 8B / a / Solution

For a type-two generating function, compare

d F_{2} = p d q + Q d P

with

d F_{2} = \frac{\partial F _{2}}{\partial q}, d q + \frac{\partial F _{2}}{\partial P}, d P .

The coefficients give the canonical-transformation equations

p = \frac{\partial F _{2}}{\partial q}, Q = \frac{\partial F _{2}}{\partial P} .

Solved by gpt-5.6-sol high.

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