Augustin-Louis Cauchy

Augustin Cauchy (1789-1857) was a prolific mathematician whose 200th birthday is commemorated on this French stamp. Besides his portrait, we see the Cauchy integral formula at right: the Cauchy integral of a regular analytic function f(z) of a complex variable is evaluated along a closed, smooth curve L in a domain D. Several paths are indicated, all enclosing the pole a. The value of these contour integrals is f(a) while contour integrals of a function not enclosing a pole are all equal to zero. On the left side of the stamp is another type of Cauchy integral, this time of a real variable, x. The function is a parabola, y=x2, and the definite integral is over the span -1=< x =<+1. It can be written as a limit as the increments along the x axis approach 0.

* Cauchy, Augustin-Louis

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