A holomorphic function is a synonym for analytic function, regular function, differentiable function, complex differentiable function, and holomorphic map (Krantz 1999, p. 16). The word derives from the Greek (holos), meaning "whole," and (morphe), meaning "form" or "appearance."

Many mathematicians prefer the term "holomorphic function" (or "holomorphic map") to "analytic function" (Krantz 1999, p. 16), while "analytic" appears to be in widespread use among physicists, engineers, and in some older texts (Morse and Feshbach 1953, pp. 356-374; Knopp 1996, pp. 83-111; Whittaker and Watson 1990, p. 83).

See also

Analytic Function, Complex Differentiable, Holonomic Function, Homeomorphic, Hyperfunction, Meromorphic Function, Regular Function

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References

Knopp, K. "Analytic Continuation and Complete Definition of Analytic Functions." Ch. 8 in Theory of Functions Parts I and II, Two Volumes Bound as One, Part I. New York: Dover, pp. 83-111, 1996.Krantz, S. G. "Holomorphic Functions." §1.3 in Handbook of Complex Variables. Boston, MA: Birkhäuser, pp. 12-16, 1999.Morse, P. M. and Feshbach, H. "Analytic Functions." §4.2 in Methods of Theoretical Physics, Part I. New York: McGraw-Hill, pp. 356-374, 1953.Whittaker, E. T. and Watson, G. N. A Course in Modern Analysis, 4th ed. Cambridge, England: Cambridge University Press, 1990.

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Holomorphic Function

Cite this as:

Weisstein, Eric W. "Holomorphic Function." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/HolomorphicFunction.html

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