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Arctangent series. In mathematics, the arctangent series, traditionally called Gregory's series, is the Taylor series expansion at the origin of the arctangent function: [1] This series converges in the complex disk except for (where ).
Series expansion. An animation showing the cosine function being approximated by successive truncations of its Maclaurin series. In mathematics, a series expansion is a technique that expresses a function as an infinite sum, or series, of simpler functions. It is a method for calculating a function that cannot be expressed by just elementary ...
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.
Polynomial expansion. In mathematics, an expansion of a product of sums expresses it as a sum of products by using the fact that multiplication distributes over addition. Expansion of a polynomial expression can be obtained by repeatedly replacing subexpressions that multiply two other subexpressions, at least one of which is an addition, by ...
The function e (−1/x 2) is not analytic at x = 0: the Taylor series is identically 0, although the function is not. If f ( x ) is given by a convergent power series in an open disk centred at b in the complex plane (or an interval in the real line), it is said to be analytic in this region.
Sears–Haack body. The Sears–Haack body is the shape with the lowest theoretical wave drag in supersonic flow, for a slender solid body or revolution with a given body length and volume. The mathematical derivation assumes small-disturbance (linearized) supersonic flow, which is governed by the Prandtl–Glauert equation.
The product integral satisfies a collection of properties defining a one-parameter continuous group; these are stated in two articles showing applications: the Dyson series and the Peano–Baker series. Commutative case. The commutative case is vastly simpler, and, as a result, a large variety of distinct notations and definitions have appeared.
These Basic Earbuds. The Work Earbuds Classic. Raycon. For everyday wear that’s easy to take in and out, these buds are the perfect pick! See it! Get The Work Earbuds Classic (originally $120 ...
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