Multiple-Valued Function

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Related to Multivalued function: Single-valued function

Multiple-Valued Function

 

a function that takes on several values for the same value of the argument. Multiple-valued functions arise when we invert single-valued functions whose values repeat. Thus, the function x2 takes on every positive value twice (for values of the argument differing only in sign); its inverse is the two-valued function Multiple-valued Function The function sin x takes on each of its values an infinite number of times; its inverse is the infinite-valued function arcs in x. Multiple-valued functions play an important role in the theory of analytic functions of a complex variable. In the complex domain, Multiple-valued Function has n values for any z ≠ 0, and f(z) = ln z, when z ≠ 0, has an infinite number of values.

References in periodicals archive ?
Perhaps, in the first time students meet with the concept of multivalued functions when dealing with the quadratic formula.
Teodoru, Continuous selections for multivalued functions, Itinerant Seminar on Functional Equations, Approximation and Convexity, Cluj-Napoca, 1986, 273-278.