# Integral-function sentence example

The discriminant is the resultant of ax and ax and of degree 8 in the coefficients; since it is a rational and

**integral function**of the fundamental invariants it is expressible as a linear function of A 2 and B; it is independent of C, and is therefore unaltered when C vanishes; we may therefore take f in the canonical form 6R 4 f = BS5+5BS4p-4A2p5.Every other concomitant is a rational

**integral function**of these four forms. The linear covariant, obviously the Jacobian of a x and x x is the line perpendicular to x and the vanishing of the quadrinvariant a x is the condition that a x passes through one of the circular points at infinity.In general any pencil of lines, connected with the line a x by descriptive or metrical properties, has for its equation a rational

**integral function**of the four forms equated to zero.Then, since nr rl is also a rational

**integral function**of n of degree r, we can find a coefficient c r, not containing n, and such as to make N-c r nr ri contain no power of n higher than n r - 1.Thus log x is the

**integral function**of 1/x, and it can be shown that log x is a genuinely new transcendent, not expressible in finite terms by means of functions such as algebraical or circular functions.Advertisement