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  2. Colin Maclaurin - Wikipedia

    en.wikipedia.org/wiki/Colin_Maclaurin

    Maclaurin attributed the series to Brook Taylor, though the series was known before to Newton and Gregory, and in special cases to Madhava of Sangamagrama in fourteenth century India. [6] Nevertheless, Maclaurin received credit for his use of the series, and the Taylor series expanded around 0 is sometimes known as the Maclaurin series. [7]

  3. Taylor series - Wikipedia

    en.wikipedia.org/wiki/Taylor_series

    The Taylor series of any polynomial is the polynomial itself.. The Maclaurin series of ⁠ 1 / 1 − x ⁠ is the geometric series + + + +. So, by substituting x for 1 − x, the Taylor series of ⁠ 1 / x ⁠ at a = 1 is

  4. Series expansion - Wikipedia

    en.wikipedia.org/wiki/Series_expansion

    A Laurent series is a generalization of the Taylor series, allowing terms with negative exponents; it takes the form = and converges in an annulus. [6] In particular, a Laurent series can be used to examine the behavior of a complex function near a singularity by considering the series expansion on an annulus centered at the singularity.

  5. 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.

  6. Euler–Maclaurin formula - Wikipedia

    en.wikipedia.org/wiki/Euler–Maclaurin_formula

    In mathematics, the Euler–Maclaurin formula is a formula for the difference between an integral and a closely related sum. It can be used to approximate integrals by finite sums, or conversely to evaluate finite sums and infinite series using integrals and the machinery of calculus .

  7. Maclaurin series - Wikipedia

    en.wikipedia.org/?title=Maclaurin_series&redirect=no

    Series expansions This page was last edited on 29 October 2015, at 21:05 (UTC) . Text is available under the Creative Commons Attribution-ShareAlike 4.0 License ; additional terms may apply.

  8. Error function - Wikipedia

    en.wikipedia.org/wiki/Error_function

    For any real x, Newton's method can be used to compute erfi −1 x, and for −1 ≤ x ≤ 1, the following Maclaurin series converges: ⁡ = = + +, where c k is defined as above. Asymptotic expansion

  9. Generating function - Wikipedia

    en.wikipedia.org/wiki/Generating_function

    The left-hand side is the Maclaurin series expansion of the right-hand side. Alternatively, the equality can be justified by multiplying the power series on the left by 1 − x, and checking that the result is the constant power series 1 (in other words, that all coefficients except the one of x 0 are equal to 0). Moreover, there can be no ...