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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.
The geometric series is an infinite series derived from a special type of sequence called a geometric progression.This means that it is the sum of infinitely many terms of geometric progression: starting from the initial term , and the next one being the initial term multiplied by a constant number known as the common ratio .
In general, any infinite series is the limit of its partial sums. For example, an analytic function is the limit of its Taylor series, within its radius of convergence. = =. This is known as the harmonic series. [6]
Mathematicians from the Kerala school were studying infinite series c. 1350 CE. [82] In the 17th century, James Gregory worked in the new decimal system on infinite series and published several Maclaurin series. In 1715, a general method for constructing the Taylor series for all functions for which they exist was provided by Brook Taylor.
Ramanujan summation is a technique invented by the mathematician Srinivasa Ramanujan for assigning a value to divergent infinite series.Although the Ramanujan summation of a divergent series is not a sum in the traditional sense, it has properties that make it mathematically useful in the study of divergent infinite series, for which conventional summation is undefined.
This article lists mathematical identities, that is, identically true relations holding in mathematics. Bézout's identity (despite its usual name, it is not, properly speaking, an identity) Binet-cauchy identity; Binomial inverse theorem; Binomial identity; Brahmagupta–Fibonacci two-square identity; Candido's identity; Cassini and Catalan ...
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