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2. Partial fraction decomposition - Wikipedia

   en.wikipedia.org/wiki/Partial_fraction_decomposition

   The concept was discovered independently in 1702 by both Johann Bernoulli and Gottfried Leibniz. [3] In symbols, the partial fraction decomposition of a rational fraction of the form where f and g are polynomials, is the expression of the rational fraction as. {\displaystyle {\frac {f (x)} {g (x)}}=p (x)+\sum _ {j} {\frac {f_ {j} (x)} {g_ {j ...

3. Continued fraction (generalized) - Wikipedia

   en.wikipedia.org/wiki/Continued_fraction...

   For the folded general continued fractions of both expressions, the rate convergence μ = (3 − √ 8) 2 = 17 − √ 288 ≈ 0.02943725, hence ⁠ 1 / μ ⁠ = (3 + √ 8) 2 = 17 + √ 288 ≈ 33.97056, whose common logarithm is 1.531... ≈ ⁠ 26 / 17 ⁠ > ⁠ 3 / 2 ⁠, thus adding at least three digits per two terms. This is because the ...

4. Continued fraction - Wikipedia

   en.wikipedia.org/wiki/Continued_fraction

   The coefficients beyond the last in any of these representations should be interpreted as +∞; and the best rational will be one of z(x 1, y 1), z(x 1, y 2), z(x 2, y 1), or z(x 2, y 2). For example, the decimal representation 3.1416 could be rounded from any number in the interval [3.14155, 3.14165) .

5. Solving quadratic equations with continued fractions - Wikipedia

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

   Solving quadratic equations with continued fractions. In mathematics, a quadratic equation is a polynomial equation of the second degree. The general form is. where a ≠ 0. The quadratic equation on a number can be solved using the well-known quadratic formula, which can be derived by completing the square. That formula always gives the roots ...

6. Heaviside cover-up method - Wikipedia

   en.wikipedia.org/wiki/Heaviside_cover-up_method

   Set up a partial fraction for each factor in the denominator. With this framework we apply the cover-up rule to solve for A, B, and C. D 1 is x + 1; set it equal to zero. This gives the residue for A when x = −1. Next, substitute this value of x into the fractional expression, but without D 1. Put this value down as the value of A.

7. Quadratic formula - Wikipedia

   en.wikipedia.org/wiki/Quadratic_formula

   Quadratic formula. The roots of the quadratic function y = ⁠ 1 2 ⁠x2 − 3x + ⁠ 5 2 ⁠ are the places where the graph intersects the x -axis, the values x = 1 and x = 5. They can be found via the quadratic formula. In elementary algebra, the quadratic formula is a closed-form expression describing the solutions of a quadratic equation.