Lectures Introductory to the Theory of Functions of Two Complex Variables Deliv
Lectures Introductory to the Theory of Functions of Two Complex Variables Deliv
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In our eReader you can find the full English version of the book. Read Lectures Introductory to the Theory of Functions of Two Complex Variables Deliv Online - link to read the book on full screen. Our eReader also allows you to upload and read Pdf, Txt, ePub and fb2 books. In the Mini eReder on the page below you can quickly view all pages of the book - Read Book Lectures Introductory to the Theory of Functions of Two Complex Variables Deliv
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f It is established for the case of n variables, Weierstrass, Ges. Werke, t. Ii, pp. 62 — 64.
124] PERIODS 215 Next, suppose that our uniform analytic function is not expressible in a form F(az + a'z') for any constants a and a' whatever; and consider a region in the field of variation where the function f(z, z) is regular. No relation oz dz for non-vanishing values of a and a, is satisfied over the whole of this region ; hence we can take places z x and */, z 2 and z 2 within the region, such ...that I Jia |, where "12 — 9 /Qi, -Q d/Pi, V ) a*! ' a*/ a/p 2, V) a/p 2, «/) t/io dz 2 dz 2 is finite and not zero. Also when we take places z 1 + u x and z/ 4- «/, z* + u^ and */ + u 2, z x + v^ and z( + v x ', z 2 + v 2 and ^ 2 ' + v 2, where all the quantities I Mi 1 1 I ^/ I » I ^2 1, I V I, I v 1 1, | v/ 1, | v 2 1, | v 2 ' | are infinitesimally small, the quantity j J l2, | where dfjZt + Ui, Zi + t> s/ + Vi) dZi dzi df(z 2 4- u 2, z 2 + m 2 ') 9/p 2 + p 2, z 2 '+v 2 ) dz 2 dz 2 differs from j J 12 j only infinitesimally, and therefore its modulus is finite and not zero.
What to read after Lectures Introductory to the Theory of Functions of Two Complex Variables Deliv?
You can find similar books in the "Read Also" column, or choose other free books by Forsyth, Andrew Russell, 1858-1942 to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
f It is established for the case of n variables, Weierstrass, Ges. Werke, t. Ii, pp. 62 — 64.
124] PERIODS 215 Next, suppose that our uniform analytic function is not expressible in a form F(az + a'z') for any constants a and a' whatever; and consider a region in the field of variation where the function f(z, z) is regular. No relation oz dz for non-vanishing values of a and a, is satisfied over the whole of this region ; hence we can take places z x and */, z 2 and z 2 within the region, such ...that I Jia |, where "12 — 9 /Qi, -Q d/Pi, V ) a*! ' a*/ a/p 2, V) a/p 2, «/) t/io dz 2 dz 2 is finite and not zero. Also when we take places z 1 + u x and z/ 4- «/, z* + u^ and */ + u 2, z x + v^ and z( + v x ', z 2 + v 2 and ^ 2 ' + v 2, where all the quantities I Mi 1 1 I ^/ I » I ^2 1, I V I, I v 1 1, | v/ 1, | v 2 1, | v 2 ' | are infinitesimally small, the quantity j J l2, | where dfjZt + Ui, Zi + t> s/ + Vi) dZi dzi df(z 2 4- u 2, z 2 + m 2 ') 9/p 2 + p 2, z 2 '+v 2 ) dz 2 dz 2 differs from j J 12 j only infinitesimally, and therefore its modulus is finite and not zero.
What to read after Lectures Introductory to the Theory of Functions of Two Complex Variables Deliv?
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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