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The absolute Galois group of the real numbers is a cyclic group of order 2 generated by complex conjugation, since C is the separable closure of R and [C:R] = 2.. In mathematics, the absolute Galois group G K of a field K is the Galois group of K sep over K, where K sep is a separable closure of K.
The threefold Cauchy product of 1 − 1 + 1 − 1 + ... is 1 − 3 + 6 − 10 + ..., the alternating series of triangular numbers; its Abel and Euler sum is 1 ⁄ 8. [16] The fourfold Cauchy product of 1 − 1 + 1 − 1 + ... is 1 − 4 + 10 − 20 + ..., the alternating series of tetrahedral numbers , whose Abel sum is 1 ⁄ 16 .
In 2017, it was proven [15] that there exists a unique function F which is a solution of the equation F(z + 1) = exp(F(z)) and satisfies the additional conditions that F(0) = 1 and F(z) approaches the fixed points of the logarithm (roughly 0.318 ± 1.337i) as z approaches ±i∞ and that F is holomorphic in the whole complex z-plane, except the ...
World production of ethanol in 2006 was 51 gigalitres (1.3 × 10 10 US gal), with 69% of the world supply coming from Brazil and the U.S. [18] Brazilian ethanol is produced from sugarcane, which has relatively high yields (830% more fuel than the fossil fuels used to produce it) compared to some other energy crops. [101]