In algebra, the partial fraction decomposition or partial fraction expansion of a rational fraction (that is, a fraction such that the numerator and the...
34 KB (7,004 words) - 13:07, 28 June 2024
_{k=0}^{n}{\binom {n}{k}}=\prod _{k=1}^{n}k^{2k-n-1}.} The partial fraction decomposition of the reciprocal is given by 1 ( z n ) = ∑ i = 0 n − 1 ( −...
61 KB (10,577 words) - 15:58, 14 August 2024
{\displaystyle {\frac {z^{3}-{\tfrac {1}{3}}a}{z^{2}-z^{3}}}.} Partial fraction decomposition Lal, Bansi (2006). Topics in Integral Calculus. Laxmi Publications...
5 KB (739 words) - 19:35, 30 January 2024
Integral of the secant function (section By partial fractions and a substitution (Barrow's approach))
1 ( 1 + u ) ( 1 − u ) d u = ∫ 1 2 ( 1 1 + u + 1 1 − u ) d u partial fraction decomposition = 1 2 ( ln | 1 + u | − ln | 1 − u | ) + C = 1 2 ln | 1...
22 KB (3,906 words) - 02:57, 5 August 2024
computation of antiderivatives of rational functions (see partial fraction decomposition for more). A fraction may also contain radicals in the numerator or the...
66 KB (9,584 words) - 20:41, 26 April 2024
latter construction may be simplified by using, as follows, partial fraction decomposition instead of the extended Euclidean algorithm. Thus, we want to...
42 KB (7,184 words) - 16:57, 12 April 2024
recordable optical disc format PFD allowance in work systems Partial fraction decomposition Perfluorodecalin, a molecule capable of dissolving large amounts...
1 KB (148 words) - 03:47, 15 April 2024
Field of fractions Partial fraction decomposition Partial fractions in integration Function field of an algebraic variety Algebraic fractions – a generalization...
16 KB (2,355 words) - 15:52, 3 June 2024
Fibonacci sequence (section Decomposition of powers)
because of the defining Fibonacci recurrence relation. The partial fraction decomposition is given by s ( z ) = 1 5 ( 1 1 − φ z − 1 1 − ψ z ) {\displaystyle...
85 KB (12,919 words) - 17:24, 14 August 2024
with appropriate scaling, can be represented as an infinite partial fraction decomposition as the sum of reciprocal functions translated by imaginary integers:...
29 KB (4,090 words) - 05:25, 23 July 2024