Read e-book online An Introduction To The Theory Of Multiply Periodic Functions PDF

By H. F. Baker

ISBN-10: 1418167037

ISBN-13: 9781418167035

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Example text

When X, is not zero, there are two places at infinity; the neighbourhood of either of these is represented by a pair of equations such as , where Vx6 has one of two signs by substitution we ; find the terms not written involving positive integral powers of t. Thus each is not infinite at but integral logarithmically, algebraically, infinity, in each sheet, the first integral to the second order, and the second integral to the x a x a first order, and it is not possible to find a linear -tp2 L 3 aggregate p l L l ' > which does not become infinite.

A qi, [CHAP. iift 17,, ft, = w'uft + w'sift + Vuft + Vaft, ft = 0>' ^i + W'fflpa + 1/Mft + Vsift, Qi ]2 PL so that PU, ft, ft are the periods of the integral + ^w *. - },,*. , )(p,',p2 ', = ? J ') 2i', -i 7 "' e K> 4(/'j. i. ,')= -^irie^p,, p,, g,, > q,, ft)(/>i'> />*' 9i'. ) - (ft, ft. , q$. - by Jirt', ft', ft') for all values , Finally, in view of subsequent work, detail the relations affecting o> and u>' it desirable to notice in is only. The relation ') u Uv Let now ft> , /O &>' - 1\ /w \ = (ft)', - to) /w \ = o)'o) - ft)ft)' = 0.

7, (1)). J are determinable uniquely, so that, M M and integers , on the dissected surface v/>- m > m + vf ' = e* + M. + 2 + Af/Tj, there being exception only for a connected sequence of values of e l and e c m of one dimension, those namely for which (tf e) vanishes for all positions of (x) these values will be expressed below in terms of one arbitrary ' ; For such exceptional values the equations are but by an infinite number of sets of positions of (zj) and parameter. still fact, (z2 ). 2 are integers.

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An Introduction To The Theory Of Multiply Periodic Functions by H. F. Baker

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