single-valued

[ sing-guhl-val-yood ]

adjective

, Mathematics.

1. (of a function) having the property that each element in the domain has corresponding to it exactly one element in the range.

Word History and Origins

Origin of single-valued¹

First recorded in 1875–80

Example Sentences

The series is evidently single-valued for any given value of ξ.

From Project Gutenberg

But it is to be remarked that there is no ground for believing, if this method of continuation be utilized, that the function is single-valued; we may quite well return to the same values of the independent variables with a different Singular points of solutions. value of the function; belonging, as we say, to a different branch of the function; and there is even no reason for assuming that the number of branches is finite, or that different branches have the same singular points and regions of existence.

From Project Gutenberg

A single-valued branch of such integral can be obtained by making a barrier in the plane joining ∞ to 0 and 1 to ∞; for instance, by excluding the consideration of real negative values of x and of real 237 positive values greater than 1, and defining the phase of x and x − 1 for real values between 0 and 1 as respectively 0 and π.

From Project Gutenberg

We may then attempt to investigate, in general, in what cases the independent variable x of a hypergeometric equation is a single-valued function of the ratio s of two independent integrals of the equation.

From Project Gutenberg

We shall understand then, by the condition that x is to be a single-valued function of x, that the region in the ς-plane corresponding to any branch is not to overlap itself, and that no two of the regions corresponding to the different branches are to overlap.

From Project Gutenberg