rational function

noun

Mathematics.

1. a function that can be written as the quotient of two polynomials with integral coefficients.

Word History and Origins

Origin of rational function¹

First recorded in 1880–85

Example Sentences

A rational function is the ratio of two polynomials.

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Thus the operations which consist in replacing x by nx and by x/n respectively, in any rational function of x, are definite inverse operations, if n is any assigned number except zero.

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On the contrary, the operation of replacing x by an assigned number in any rational function of x is not, in the present sense, although it leads to a unique result, a definite operation; there is in fact no unique inverse operation corresponding to it.

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But, in fact, if J, J1 denote any two of the three integrals J1, J2, J3, there exists an equation AJ + BJ′ + Cƒs−1dz = rational function of s, z, where A, B, C are properly chosen constants.

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This being so, a single valued function of u1, ... up without essential singularities for infinite or finite values of the variables can be shown, by induction, to be, as in the case of p = 1, necessarily a rational function of the variables.

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