# Xn

Xn Christian

Origin of Xn

see XP- Thus ortho-phenylene diamine yields the following products: N H N ./`N;
**Xn**NZ In some cases oxidation of condensed benzenoid-heterocyclic nuclei results in the rupture of the heterocyclic ring with the formation of a benzene dicarboxylic acid; but if the aromatic nucleus be weakened by the introduction of an amino group, then it is the benzenoid nucleus which is destroyed and a dicarboxylic acid of the heterocyclic ring system obtained. - In general in space of n dimensions we have n substitutions similar to X l = a11x1 +a12x2 + ï¿½ ï¿½ ï¿½ + ainxn, and we have to express the n 2 coefficients in terms of Zn(n - I)i independent quantities; which must be possible, because X1+X2+..."IL
**Xn**=xi+x2 +x3 +...+4. - =0, are non-unitary symmetric functions of the roots of a
**xn-a**l**xn**1 a2 x n-2 -... - The binomial theorem may, for instance, be stated for (x+a)n alone; the formula for (x-a)" being obtained by writing it as {x+(-)a} n or Ix+(- a) } n, so that (x-a) n =x"- 1)
**xn-laF**...+(-)rn(r)**xn-rar**+..., where + (-) r means - or + according as r is odd or even. - This is expressed by saying that the sequence converges to (x+h)" as its limit; it may be stated concisely in any of the three ways, (x+h) n =lim(x"+n(1)
**xn-lh**+....+ n(T)**xn-rhr**+ï¿½ï¿½.),(x+h)n =lim Sr, Sr. (x+h)n.

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