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  2. Arctangent series - Wikipedia

    en.wikipedia.org/wiki/Arctangent_series

    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 ).

  3. Taylor series - Wikipedia

    en.wikipedia.org/wiki/Taylor_series

    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.

  4. Aluminium compounds - Wikipedia

    en.wikipedia.org/wiki/Aluminium_compounds

    The vast majority of compounds, including all aluminium-containing minerals and all commercially significant aluminium compounds, feature aluminium in the oxidation state 3+. The coordination number of such compounds varies, but generally Al 3+ is either six- or four-coordinate. Almost all compounds of aluminium (III) are colorless.

  5. Series expansion - Wikipedia

    en.wikipedia.org/wiki/Series_expansion

    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 ...

  6. Aluminium–lithium alloys - Wikipedia

    en.wikipedia.org/wiki/Aluminium–lithium_alloys

    The Al 3 Li structure is known as the AuCu 3, L1 2, or Pm 3 m and has a lattice parameter of 4.01 Å. The Al–Li structure is known as the NaTl, B32, or Fd 3 m structure, which is made of both lithium and aluminium assuming diamond structures and has a lattice parameter of 6.37 Å. The interatomic spacing for Al–Li (3.19 Å) is smaller than ...

  7. 1 − 2 + 3 − 4 + ⋯ - Wikipedia

    en.wikipedia.org/wiki/1_%E2%88%92_2_%2B_3_%E2%88...

    The idea becomes clearer by considering the general series 1 − 2x + 3x 2 − 4x 3 + 5x 4 − 6x 5 + &c. that arises while expanding the expression 1 ⁄ (1+x) 2, which this series is indeed equal to after we set x = 1.

  8. Hall–Héroult process - Wikipedia

    en.wikipedia.org/wiki/Hall–Héroult_process

    In industrial production, AlF 3 is added so that the cryolite ratio is 23 to further reduce the melting point, so that the electrolysis can happen at temperatures between 940 and 980 °C (1700 to 1800°F). The density of liquid aluminum is 2.3 g/ml at temperatures between 950 and 1000 °C (1750° to 1830°F).

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