becomes a partial differential equation to be satisfied by S. It has
been shown by Jacobi that the dynamical problem resolves itself into
obtaining a "complete" solution of this equation, involving n + 1
arbitrary constants. This aspect of the subject, as a problem in
partial differential equations, has received great attention at the
hands of mathematicians, but must be passed over here.
Characteristic function.
There is a similar theory for the function
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A = 2 | Tdt = S + H[tau] (8)
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