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  2. Series (mathematics) - Wikipedia

    en.wikipedia.org/wiki/Series_(mathematics)

    In mathematics, a series is, roughly speaking, an addition of infinitely many terms, one after the other. [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 in combinatorics through generating functions.

  3. Convergent series - Wikipedia

    en.wikipedia.org/wiki/Convergent_series

    The Maclaurin series of the logarithm function ⁡ (+) is conditionally convergent for x = 1. The Riemann series theorem states that if a series converges conditionally, it is possible to rearrange the terms of the series in such a way that the series converges to any value, or even diverges.

  4. Category:Sequences and series - Wikipedia

    en.wikipedia.org/wiki/Category:Sequences_and_series

    A series is a sum of a sequence of terms. That is, a series is a list of numbers with addition operations between them. Subcategories. This category has the following ...

  5. Sequence - Wikipedia

    en.wikipedia.org/wiki/Sequence

    A series is, informally speaking, the sum of the terms of a sequence. That is, it is an expression of the form ∑ n = 1 ∞ a n {\textstyle \sum _{n=1}^{\infty }a_{n}} or a 1 + a 2 + ⋯ {\displaystyle a_{1}+a_{2}+\cdots } , where ( a n ) {\displaystyle (a_{n})} is a sequence of real or complex numbers.

  6. Power series - Wikipedia

    en.wikipedia.org/wiki/Power_series

    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 .

  7. Taylor series - Wikipedia

    en.wikipedia.org/wiki/Taylor_series

    That is, the Taylor series diverges at x if the distance between x and b is larger than the radius of convergence. The Taylor series can be used to calculate the value of an entire function at every point, if the value of the function, and of all of its derivatives, are known at a single point. Uses of the Taylor series for analytic functions ...

  8. Recurrence relation - Wikipedia

    en.wikipedia.org/wiki/Recurrence_relation

    In mathematics, a recurrence relation is an equation according to which the th term of a sequence of numbers is equal to some combination of the previous terms. Often, only previous terms of the sequence appear in the equation, for a parameter that is independent of ; this number is called the order of the relation.

  9. Generating function - Wikipedia

    en.wikipedia.org/wiki/Generating_function

    There are various types of generating functions, including ordinary generating functions, exponential generating functions, Lambert series, Bell series, and Dirichlet series. Every sequence in principle has a generating function of each type (except that Lambert and Dirichlet series require indices to start at 1 rather than 0), but the ease ...