Theory of Functions of a Complex Variable
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208 MULTIPLE [109.
Hence we have Ao) 1 =/i0 2 — c'Oj, Aa> 2 — XOi — eQ 2 - Since X and p are both greater than A, let \ = X 1 A+X', /i = ii 1 A + ijl', where X' and p.' are'-ee' = AA'; then X' and p' are >A' and are prime to it. And now A (a>! — ^1^2) = /*'^2 ~ e '^l> ^ (^2 — ^1^1) ~ X'flj — ei2 2 5 and therefore, if which are periods, we have AQ 3 =//122 — e '^i? Ai2 4 =X'Q 1 — eS2 2 * With 3 and Q 4 we can construct a parallelogram smaller than that constructed with Qj and Q 2 .
W ...e now have A'Q 1 = eQ 3 +/i'0 4 , A'Q 2 =X'Q 3 + e'G 4 , that is, equations of the same form as before. We proceed thus in successive stages : each quantity A thus obtained is distinctly less than the preceding A, and so finally we shall reach a stage when the succeeding A would be unity, that is, the solution of the pair of equations then leads to periods that determine a fundamental parallelogram.
What to read after Theory of Functions of a Complex Variable?
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To quickly assess the difficulty of the text, read a short excerpt:
208 MULTIPLE [109.
Hence we have Ao) 1 =/i0 2 — c'Oj, Aa> 2 — XOi — eQ 2 - Since X and p are both greater than A, let \ = X 1 A+X', /i = ii 1 A + ijl', where X' and p.' are
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What to read after Theory of Functions of a Complex Variable?
You can find similar books in the "Read Also" column, or choose other free books by Forsyth, Andrew Russell, 1858-1942 to read onlineMoreLess
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