# List of Mathematical Series - Rational Functions

Rational Functions

• An infinite series of any rational function of can be reduced to a finite series of polygamma functions, by use of partial fraction decomposition. This fact can also be applied to finite series of rational functions, allowing the result to be computed in constant time even when the series contains a large number of terms.

### Other articles related to "rational functions, function, functions, rational function":

Liouville's Theorem (differential Algebra) - Examples
... As an example, the field C(x) of rational functions in a single variable has a derivation given by the standard derivative with respect to that variable ... The function, which exists in C(x), does not have an antiderivative in C(x) ... Likewise, the function does not have an antiderivative in C(x) ...
Algebraic Geometry - Basic Notions - Rational Function and Birational Equivalence
... projective completion have the same field of functions ... field of fractions which is denoted k(V) and called the field of the rational functions on V or, shortly, the function field of V ... Its elements are the restrictions to V of the rational functions over the affine space containing V ...
Polynomial And Rational Function Modeling - Rational Function Models - Advantages
... Rational function models have the following advantages Rational function models have a moderately simple form ... Rational function models are a closed family ... As with polynomial models, this means that rational function models are not dependent on the underlying metric ...

### Famous quotes containing the words functions and/or rational:

Mark the babe
Not long accustomed to this breathing world;
One that hath barely learned to shape a smile,
Though yet irrational of soul, to grasp
With tiny finger—to let fall a tear;
And, as the heavy cloud of sleep dissolves,
To stretch his limbs, bemocking, as might seem,
The outward functions of intelligent man.
William Wordsworth (1770–1850)

No actual skeptic, so far as I know, has claimed to disbelieve in an objective world. Skepticism is not a denial of belief, but rather a denial of rational grounds for belief.
William Pepperell Montague (1842–1910)