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List of mathematical series. This list of mathematical series contains formulae for finite and infinite sums. It can be used in conjunction with other tools for evaluating sums. is a Bernoulli polynomial. is an Euler number. is the Riemann zeta function. is the gamma function. is a polygamma function. is a polylogarithm.
In mathematics, a series is, roughly speaking, the operation of adding infinitely many quantities, one after the other, to a given starting quantity. [ 1] The study of series is a major part of calculus and its generalization, mathematical analysis. Series are used in most areas of mathematics, even for studying finite structures (such as in ...
In mathematics, the harmonic series is the infinite series formed by summing all positive unit fractions : The first terms of the series sum to approximately , where is the natural logarithm and is the Euler–Mascheroni constant. Because the logarithm has arbitrarily large values, the harmonic series does not have a finite limit: it is a ...
In mathematics, a geometric series is a series in which the ratio of ... lengths of specific line segments from different terms in the series. For example, ...
Fourier transforms. A Fourier series ( / ˈfʊrieɪ, - iər / [ 1]) is an expansion of a periodic function into a sum of trigonometric functions. The Fourier series is an example of a trigonometric series, but not all trigonometric series are Fourier series. [ 2] By expressing a function as a sum of sines and cosines, many problems involving ...
Power series. In mathematics, a power series (in one variable) is an infinite series of the form where an represents the coefficient of the n th term and c is a constant. Power series are useful in mathematical analysis, where they arise as Taylor series of infinitely differentiable functions.
In mathematics, a series is the sum of the terms of an infinite sequence of numbers. More precisely, an infinite sequence defines a series S that is denoted. The n th partial sum Sn is the sum of the first n terms of the sequence; that is, A series is convergent (or converges) if and only if the sequence of its partial sums tends to a limit ...
Telescoping series. In mathematics, a telescoping series is a series whose general term is of the form , i.e. the difference of two consecutive terms of a sequence . [ 1] As a consequence the partial sums only consists of two terms of after cancellation. [ 2][ 3] The cancellation technique, with part of each term cancelling with part of the ...
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