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sense by the sum of first-kind Chebyshev polynomials T,(x):
Find the value of a,.
f(x)=aoTo+ a\T\ + a 2 T 2 + a,T,+a 4 T 4 •
2.21. Given the function of two variables
F(x\ ,x 2 )=612-60x\-132x 2 + 13x;-lOx\x 2 + 13xL
Problems 33
find the values of XI and x 2
at the extreme valueby equating the first
partial derivatives to zero.
2.22. Given the fitting-function form
Z(s)
a O +a l s+azs 2
l+b,s+b 2
s 2 +b J
s' '
write the third equation from the appropriate set from Figure 2.10.
2.23. Discrete, complex numerical data can be fitted versus frequency by a
rational polynomial. For the polynomial
ao+ a 1 s+ a 2 s 2 + a 3 s 3o + a 4 s 4
Z(s) = 2 J 4 , '
1+ b,s+ b 2 s + b,s + b 4 s + b,s
write the first and last linear equations that result from Levy's method
in terms of constants ~\, Sj. T j • and Vi for i= 0.1, ....