Theory of the Algebraic Functions of a Complex Variable
The book Theory of the Algebraic Functions of a Complex Variable was written by author John Charles Fields Here you can read free online of Theory of the Algebraic Functions of a Complex Variable book, rate and share your impressions in comments. If you don't know what to write, just answer the question: Why is Theory of the Algebraic Functions of a Complex Variable a good or bad book?
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85 (5) i/(z,v).ff(z,v).R{z,v), (8=1,. ..I) obtained on multiplying the expressions on the left of these identities by R(z, v), and the vanishing of the coefficients of (z — af~~ l v 2n ~ 2 in these I products will impose just the same conditions on the coefficients of ']> (z, v), as would the vanishing of the coefficients of (z — a) l ~~ 1 v n ~~ l in the I functions lf(z,v). In order that an integral rational function ty(z,v) should be com- plementary adjoint to the order * to the system of fu...nctions (z,v), whose orders of coincidence with the branches of the several cycles are not less than the adjoint numbers [x' l5 ... y.' r respectively, it is therefore necessary and sufficient that the coefficients of (z — a) i ~~ l v in ~ 2 in the I products (5) should all vanish. We shall now write the I products f^(z,v). R(z,v) in the form (6) ? (z, v) is made up of all terms of the product on the left which are divisible by v n ~ l and which at the same time are not divisible by (z—af.
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