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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.
Download as PDF; Printable version ... Part of a series of articles about: Calculus ′ = () Fundamental theorem ... This page was last edited on 10 February ...
In mathematics, the power series method is used to seek a power series solution to certain differential equations. In general, such a solution assumes a power series with unknown coefficients, then substitutes that solution into the differential equation to find a recurrence relation for the coefficients.
In mathematics, a power series (in one variable) is an infinite series of the form = = + + + … where represents the coefficient of the nth term and c is a constant called the center of the series. Power series are useful in mathematical analysis , where they arise as Taylor series of infinitely differentiable functions .
The power rule for integrals was first demonstrated in a geometric form by Italian mathematician Bonaventura Cavalieri in the early 17th century for all positive integer values of , and during the mid 17th century for all rational powers by the mathematicians Pierre de Fermat, Evangelista Torricelli, Gilles de Roberval, John Wallis, and Blaise ...
A power series is a series of the form ∑ n = 0 ∞ a n ( x − c ) n . {\displaystyle \sum _{n=0}^{\infty }a_{n}(x-c)^{n}.} The Taylor series at a point c {\displaystyle c} of a function is a power series that, in many cases, converges to the function in a neighborhood of c {\displaystyle c} .
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