If is analytic and its partial derivatives are continuous throughout some simply connected region , then
(1) |
(2) |
(3) |
(4) |
(5) |
(6) |
(7) |
(8) |
(9) |
(10) |
For a Multiply Connected region,
(11) |
See also Cauchy Integral Theorem, Morera's Theorem, Residue Theorem (Complex Analysis)
References
Arfken, G. ``Cauchy's Integral Theorem.'' §6.3 in Mathematical Methods for Physicists, 3rd ed. Orlando, FL:
Academic Press, pp. 365-371, 1985.
Morse, P. M. and Feshbach, H. Methods of Theoretical Physics, Part I. New York: McGraw-Hill,
pp. 363-367, 1953.
© 1996-9 Eric W. Weisstein