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2. Solving quadratic equations with continued fractions

   en.wikipedia.org/wiki/Solving_quadratic...

   Unfortunately, the discriminant b 2 − 4c is not as useful in this situation, because it may be a complex number. Still, a modified version of the general theorem can be proved. The continued fraction solution to the general monic quadratic equation with complex coefficients + + = given by

3. 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.

4. Continued fraction - Wikipedia

   en.wikipedia.org/wiki/Continued_fraction

   Lagrange's discovery implies that the canonical continued fraction expansion of the square root of every non-square integer is periodic and that, if the period is of length p > 1, it contains a palindromic string of length p − 1. In 1813 Gauss derived from complex-valued hypergeometric functions what is now called Gauss's continued fractions ...

5. 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 ...

6. Fraction - Wikipedia

   en.wikipedia.org/wiki/Fraction

   Common fractions can be positive or negative, and they can be proper or improper (see below). Compound fractions, complex fractions, mixed numerals, and decimals (see below) are not common fractions; though, unless irrational, they can be evaluated to a common fraction. A unit fraction is a common fraction with a numerator of 1 (e.g., ⁠ 1 / 7

7. Algebraic fraction - Wikipedia

   en.wikipedia.org/wiki/Algebraic_fraction

   The numerator and denominator are called the terms of the algebraic fraction. A complex fraction is a fraction whose numerator or denominator, or both, contains a fraction. A simple fraction contains no fraction either in its numerator or its denominator. A fraction is in lowest terms if the only factor common to the numerator and the ...

8. Euclidean algorithm - Wikipedia

   en.wikipedia.org/wiki/Euclidean_algorithm

   The Euclidean algorithm can be used to solve linear Diophantine equations and Chinese remainder problems for polynomials; continued fractions of polynomials can also be defined. The polynomial Euclidean algorithm has other applications, such as Sturm chains , a method for counting the zeros of a polynomial that lie inside a given real interval ...

9. Fractional calculus - Wikipedia

   en.wikipedia.org/wiki/Fractional_calculus

   Fractional calculus is a branch of mathematical analysis that studies the several different possibilities of defining real number powers or complex number powers of the differentiation operator = (), and of the integration operator J {\displaystyle J} [ Note 1 ] J f ( x ) = ∫ 0 x f ( s ) d s , {\displaystyle Jf(x)=\int _{0}^{x}f(s)\,ds\,,}