be 2k+25+1 and Oo pt, j with Ky and Yy fixed it is always possible 
to subtract and integral number of 27's from the sum in order to 
find a new '(jap5)s (short notation for V'C H oy404412% oper, 5) 
such that ¥'(3,p;) has the same probability distribution as the 
original } . 
In equation (10.11), for a fixed j, the net over 6 for this 
small subdivision of the original strip has been picked so that 
each of the terms under the square root sign in the evaluation of 
the integral has the same numerical value, given by the increment 
in E(#,7/2) from Hon4053 tO Hoy4oj40 divided by R, the total 
number of elemental areas in the small strip. This can obvious- 
ly always be done. Each term in the sum over p is thus given 
by AE,/R. 
Equations (10.10) and (10.11) are next substituted into 
equation (10.9) in order to obtain the first expression in 
equation (10.12). The cosine term is then expanded by trigo- 
nometric identity in the second expression, and the summation 
over p is moved inside. An expression of the form A cos® + B sine 
/ 
oe aos (6 | W ) and this has 
can be written in the form [A° +B 
been done in the last expression in equation (10.12). The conm- 
plete expression for W '(j) is given by equation (10.13). 
The next step is to simplify the coefficient of the cosine 
term in equation (10.13). In equation (10.14) this is done by 
writing the cosine and sine in complex notation. When the first 
expression on the right in equation (10.14) is expanded, only 
the cross product terms remain and the second expression results. 
The sum from p equals zero to R - 1 of exp(i ¥'(jsp;)) is a sum 
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