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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.
In probability theory, it is possible to approximate the moments of a function f of a random variable X using Taylor expansions, provided that f is sufficiently differentiable and that the moments of X are finite. A simulation-based alternative to this approximation is the application of Monte Carlo simulations.
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.
Countries by land border length Antarctica and countries in purple are those without any land border. This list gives the number of distinct land borders of each country or territory, as well as the neighbouring countries and territories. The length of each border is included, as is the total length of each country's or territory's borders. [1]
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Country/Countries 83-42 Greenland, Denmark: A Nova: Beira Baixa islands Portugal: Abbasak: Persian Gulf Iran: Aberdeen: Georgian Bay, Ontario Canada Abner Cay: Bahamas Bahamas: Abruka: Gulf of Riga Estonia: Absecon New Jersey United States Abu Musa: Persian Gulf: Claimed by Iran and United Arab Emirates: Acheron: Great Palm Island, Queensland ...
On Sunday, Taylor Swift officially wrapped up the Eras Tour in Vancouver after 149 shows in 21 countries, totaling about 484 hours spent performing on stage.
In mathematics, the Euler numbers are a sequence E n of integers (sequence A122045 in the OEIS) defined by the Taylor series expansion = + = =!, where is the hyperbolic cosine function.