Sentence Examples

  • ) j1+j2+j3+..� (J1+ j2 +j3+...-1)!/T1)?1(J2)72 (J 3)/3..., j11j2!j3!... ?.1 for the expression of Za n in terms of products of symmetric functions symbolized by separations of (n 1 1n 2 2n 3 3) Let (n) a, (n) x, (n) X denote the sums of the n th powers of quantities whose elementary symmetric functions are a l, a 2, a31���; x 1, x2, x31..; X1, X2, X3,...
  • (x- an), the sums of powers Ea t, Za 3, Za 4, ...Za n all satisfy the equation Si=o.
  • A quaternion is best defined as a symbol of the type q = Za s e s = aoeo + ales = ale, + a3e3, where eo, ...
  • The sum and product of two quantities are defined in the first instance by the formulae zae -IE(3e = E (a +0) e, Za,ei X E ai e j = (a iai) eie9, so that the laws A, C, D of � 3 are satisfied.
  • Put S2 1 =12 cos 4, 12 2 = -12 sin 4, d4 d52 1 dS22 Y a2+c2 122 7Ti = 71 22 CL2- c2(121+5221)J, a2 +c2 do a2+c2 + 4c2 z dt a'-c2 (a2+,c2)2 M+2c2(a2-c2 N-{-a2+c2 2 Ý_a 2 +c 2 (' 4c2 .?"d za 2 -c 2 c2)2 2'J Z M+ -c2) which, as Z is a quadratic function of i 2, are non-elliptic so also for; G, where =co cos, G, 7 7 = - sin 4.

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