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  2. Rational function - Wikipedia

    en.wikipedia.org/wiki/Rational_function

    Every Laurent polynomial can be written as a rational function while the converse is not necessarily true, i.e., the ring of Laurent polynomials is a subring of the rational functions. The rational function f ( x ) = x x {\displaystyle f(x)={\tfrac {x}{x}}} is equal to 1 for all x except 0, where there is a removable singularity .

  3. Risch algorithm - Wikipedia

    en.wikipedia.org/wiki/Risch_Algorithm

    These are functions obtained by composing exponentials, logarithms, radicals, trigonometric functions, and the four arithmetic operations (+ − × ÷). Laplace solved this problem for the case of rational functions , as he showed that the indefinite integral of a rational function is a rational function and a finite number of constant ...

  4. List of integrals of rational functions - Wikipedia

    en.wikipedia.org/wiki/List_of_integrals_of...

    The following is a list of integrals (antiderivative functions) of rational functions. Any rational function can be integrated by partial fraction decomposition of the function into a sum of functions of the form:

  5. Polynomial and rational function modeling - Wikipedia

    en.wikipedia.org/wiki/Polynomial_and_rational...

    Rational functions can be either finite or infinite for finite values, or finite or infinite for infinite x values. Thus, rational functions can easily be incorporated into a rational function model. Rational function models can often be used to model complicated structure with a fairly low degree in both the numerator and denominator.

  6. List of mathematical functions - Wikipedia

    en.wikipedia.org/wiki/List_of_mathematical_functions

    Dirichlet function: is an indicator function that matches 1 to rational numbers and 0 to irrationals. It is nowhere continuous. Thomae's function: is a function that is continuous at all irrational numbers and discontinuous at all rational numbers. It is also a modification of Dirichlet function and sometimes called Riemann function.

  7. List of arbitrary-precision arithmetic software - Wikipedia

    en.wikipedia.org/wiki/List_of_arbitrary...

    The Decimal class in the standard library module decimal has user definable precision and limited mathematical operations (exponentiation, square root, etc. but no trigonometric functions). The Fraction class in the module fractions implements rational numbers. More extensive arbitrary precision floating point arithmetic is available with the ...

  8. Padé approximant - Wikipedia

    en.wikipedia.org/wiki/Padé_approximant

    Since a Padé approximant is a rational function, an artificial singular point may occur as an approximation, but this can be avoided by Borel–Padé analysis. The reason the Padé approximant tends to be a better approximation than a truncating Taylor series is clear from the viewpoint of the multi-point summation method.

  9. Function (mathematics) - Wikipedia

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

    Rational functions are quotients of two polynomial functions, and their domain is the real numbers with a finite number of them removed to avoid division by zero. The simplest rational function is the function , whose graph is a hyperbola, and whose domain is the whole real line except for 0.