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  2. Zeros and poles - Wikipedia

    en.wikipedia.org/wiki/Zeros_and_poles

    Technically, a point z 0 is a pole of a function f if it is a zero of the function 1/f and 1/f is holomorphic (i.e. complex differentiable) in some neighbourhood of z 0. A function f is meromorphic in an open set U if for every point z of U there is a neighborhood of z in which at least one of f and 1/f is holomorphic.

  3. Milne-Thomson method for finding a holomorphic function

    en.wikipedia.org/wiki/Milne-Thomson_method_for...

    In mathematics, the Milne-Thomson method is a method for finding a holomorphic function whose real or imaginary part is given. [1] It is named after Louis Melville Milne-Thomson . Introduction

  4. Root-finding algorithm - Wikipedia

    en.wikipedia.org/wiki/Root-finding_algorithm

    In numerical analysis, a root-finding algorithm is an algorithm for finding zeros, also called "roots", of continuous functions. A zero of a function f is a number x such that f ( x ) = 0 . As, generally, the zeros of a function cannot be computed exactly nor expressed in closed form , root-finding algorithms provide approximations to zeros.

  5. Removable singularity - Wikipedia

    en.wikipedia.org/wiki/Removable_singularity

    A holomorphic function's singularity is either not really a singularity at all, i.e. a removable singularity, or one of the following two types: In light of Riemann's theorem, given a non-removable singularity, one might ask whether there exists a natural number m {\displaystyle m} such that lim z → a ( z − a ) m + 1 f ( z ) = 0 ...

  6. Maze-solving algorithm - Wikipedia

    en.wikipedia.org/wiki/Maze-solving_algorithm

    Robot in a wooden maze. A maze-solving algorithm is an automated method for solving a maze.The random mouse, wall follower, Pledge, and Trémaux's algorithms are designed to be used inside the maze by a traveler with no prior knowledge of the maze, whereas the dead-end filling and shortest path algorithms are designed to be used by a person or computer program that can see the whole maze at once.

  7. Residue (complex analysis) - Wikipedia

    en.wikipedia.org/wiki/Residue_(complex_analysis)

    It may be that the function f can be expressed as a quotient of two functions, () = (), where g and h are holomorphic functions in a neighbourhood of c, with h(c) = 0 and h'(c) ≠ 0. In such a case, L'Hôpital's rule can be used to simplify the above formula to:

  8. List of types of functions - Wikipedia

    en.wikipedia.org/wiki/List_of_types_of_functions

    Nowhere continuous function: is not continuous at any point of its domain; for example, the Dirichlet function. Homeomorphism: is a bijective function that is also continuous, and whose inverse is continuous. Open function: maps open sets to open sets. Closed function: maps closed sets to closed sets.

  9. Genus (mathematics) - Wikipedia

    en.wikipedia.org/wiki/Genus_(mathematics)

    In layman's terms, the genus is the number of "holes" an object has ("holes" interpreted in the sense of doughnut holes; a hollow sphere would be considered as having zero holes in this sense). [3] A torus has 1 such hole, while a sphere has 0. The green surface pictured above has 2 holes of the relevant sort. For instance:

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