The ramification index can be calculated explicitly from Cauchy's integral formula.
The integral formula has broad applications.
One such formula is the following integral formula involving a product of three Bessel functions:
He used this to give the following integral formula for the zeta function:
This is really a restatement of Cauchy's integral formula.
Cauchy's integral formula suggests the following definition (purely formal, for now):
More useful integral formulas for P are necessary for any practical calculation.
Note that both of these integral formulas do not converge in any usual sense for "typical" systems .
In general, derivatives of any order can be calculated using Cauchy's integral formula:
A number of integral formulas involving the eta function can be listed.