rational function

A function that can be expressed as a quotient of polynomials, excluding division by zero.

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can be expressed in terms of elementary functions if and only if there exists some rational function h such that it is a solution to the differential equation:

A New Special Function and Its Application in Probability

In recent years, some novel dispersive models have been introduced, for example, the complex-conjugate pole-residue (CCPR) model [3], critical point (CP) model [4], modified Lorentz (m-Lo) model [5], and quadratic complex rational function (QCRF) model [6].

An Extended Newmark-FDTD Method for Complex Dispersive Media

Lump solutions are a type of rational function solutions, localized in all directions in the space.

Lump Solutions to a (2+1)-Dimensional Fifth-Order KdV-Like Equation

Let R be a rational function (or a polynomial) that belongs asymptotically to [kr.sup.[alpha]] as r [right arrow] [infinity], where k [not equal to] 0, a are constants.

Normal Families and Growth of Meromorphic Functions with Their Kth Derivatives

Furthermore, for the nonlinear problem, the multiple exp-function method [18, 19], the transformed rational function method [20-22], and invariant subspace method [23, 24] are three systematical approaches to handle the nonlinear terms.

Homotopy Series Solutions to Time-Space Fractional Coupled Systems

One of them is that, given a non-constant rational function f, with rational coefficients, if [xi] is a Liouville number, then so is f([xi]).

A note on transcendental entire functions mapping uncountable many Liouville numbers into the set of Liouville numbers

where r|q - 1 and the rational function [mu](x) [member of] [F.sub.q](x) satisfies the following conditions:

p-cycles, [S.sub.2]-sets and Curves with Many Points

Several types of approximations are available in the literature, for example, by use of Functional approach, Sampling approach, Geometric approach, Weight function approach, Adomain approach, Composition approach and Rational function approach.

An Optimal Family of Eighth-Order Iterative Methods with an Inverse Interpolatory Rational Function Error Corrector for Nonlinear Equations

In [31], Ma and Lee have obtained rational solutions of (1) including travelling wave solutions, variable separated solutions, and polynomial solutions by using rational function transformation and Backlund transformation.

Theta Function Solutions of the 3 + 1-Dimensional Jimbo-Miwa Equation

This method uses the rational function of the PDN impedance in the time domain based on measurements.

Investigation and Analysis of the Simultaneous Switching Noise in Power Distribution Network with Multi-Power Supplies of High Speed CMOS Circuits

The aeroelastic equations of motion are formulated in the time-domain, through the Rational Function Approximation and application of the Balanced Truncation method.

Reduced order model approach for efficient aircraft loads prediction

and for f, g [member of] K[[X.sub.1],...,[X.sub.n]], all the degrees above may be extended for the rational function f / g as the maximum between the corresponding degrees of f and g: