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  2. Partial fraction decomposition - Wikipedia

    en.wikipedia.org/wiki/Partial_fraction_decomposition

    In algebra, the partial fraction decomposition or partial fraction expansion of a rational fraction (that is, a fraction such that the numerator and the denominator are both polynomials) is an operation that consists of expressing the fraction as a sum of a polynomial (possibly zero) and one or several fractions with a simpler denominator.

  3. Partial fractions in complex analysis - Wikipedia

    en.wikipedia.org/wiki/Partial_fractions_in...

    In complex analysis, a partial fraction expansion is a way of writing a meromorphic function as an infinite sum of rational functions and polynomials. When f ( z ) {\displaystyle f(z)} is a rational function, this reduces to the usual method of partial fractions .

  4. Heaviside cover-up method - Wikipedia

    en.wikipedia.org/wiki/Heaviside_cover-up_method

    When a partial fraction term has a single (i.e. unrepeated) binomial in the denominator, the numerator is a residue of the function defined by the input fraction. We calculate each respective numerator by (1) taking the root of the denominator (i.e. the value of x that makes the denominator zero) and (2) then substituting this root into the ...

  5. List of mathematical series - Wikipedia

    en.wikipedia.org/wiki/List_of_mathematical_series

    An infinite series of any rational function of can be reduced to a finite series of polygamma functions, by use of partial fraction decomposition, [8] as explained here. 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.

  6. Mittag-Leffler's theorem - Wikipedia

    en.wikipedia.org/wiki/Mittag-Leffler's_theorem

    Conversely, it can be used to express any meromorphic function as a sum of partial fractions. It is sister to the Weierstrass factorization theorem, which asserts existence of holomorphic functions with prescribed zeros. The theorem is named after the Swedish mathematician Gösta Mittag-Leffler who published versions of the theorem in 1876 and ...

  7. Category:Partial fractions - Wikipedia

    en.wikipedia.org/wiki/Category:Partial_fractions

    Partial fraction decomposition; Partial fractions in complex analysis This page was last edited on 4 October 2006, at 20:40 (UTC). Text is available under the ...

  8. Separation of variables - Wikipedia

    en.wikipedia.org/wiki/Separation_of_variables

    If one can evaluate the two integrals, one can find a solution to the differential equation. Observe that this process effectively allows us to treat the derivative as a fraction which can be separated. This allows us to solve separable differential equations more conveniently, as demonstrated in the example below.

  9. Raoult's law - Wikipedia

    en.wikipedia.org/wiki/Raoult's_law

    Raoult's law (/ ˈ r ɑː uː l z / law) is a relation of physical chemistry, with implications in thermodynamics.Proposed by French chemist François-Marie Raoult in 1887, [1] [2] it states that the partial pressure of each component of an ideal mixture of liquids is equal to the vapor pressure of the pure component (liquid or solid) multiplied by its mole fraction in the mixture.

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