(9.27) all of the limiting processes have been designated by the 
simple notation, lim, and the summation over n has been written 
out in full. In equation (9.28), the summation over p has also been 
written out in full, and the trigonometric terms have been desig- 
nated by a shorter notation. 
The next expression in equation (9.28) indicates the process 
of squaring the entire large bracket. Each term in the sum will 
occur as a square, and there will also be a large number of cross 
product terms. Each squared term will be of the form of the square 
of one of the indicated square roots times the square of a cosine 
term, and since, for example, (cos a)* = (1 + cos 2a)/2, a term 
equal to one half of the sums of the squares of all of the indi- 
cated square roots will occur. There will also be a great many 
terms which are periodic in either y or t or both. Some of the 
terms which are periodic in either y or t or both occur first as 
the product of two trigonometric terms. In every case, however, 
either the values of # in the two terms or the values of 9 in the 
two terms will be different, and the product can therefore be 
written as the sum of two trigonometric terms which involve the sum 
and difference of the arguments. 
The sum of all of the values of E,(# ,0) at the points of 
the net telescopes into the value of E5(H 9598p) by virtue of 
the properties of the net and the properties of E,(#,0). For 
example, the first row of terms in equation (9.28) becomes simply 
E5( 59985) All terms occur once positively in the sum and once 
negatively except £,(0,0), B(05;85), E5(H 5990) and Bo ( H55)95)- 
All but E,(f155,05) are zero by definition. The second row of 
terms, of which only the first is shown, becomes E CH5518,) = 
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