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A process of extending the region in which a Complex Function is defined.
See also Monodromy Theorem, Permanence of Algebraic Form, Permanence of Mathematical Relations Principle
References
Arfken, G.  Mathematical Methods for Physicists, 3rd ed.  Orlando, FL: Academic Press, pp. 378-380, 1985.
 
Morse, P. M. and Feshbach, H.  Methods of Theoretical Physics, Part I.  New York: McGraw-Hill,
  pp. 389-390 and 392-398, 1953.