(6.74) corresponds to the dotted line in the table.
6.8.3 Lagrange’s
4
Formula
for Unequal Intervals
Theorem 6.5 If the functional values f ( x
r
) are
known at the arguments x
r
(r = 0, 1, 2, …, n) then
12
0
01020
02
1
10121
011
011
()()()
()()
()()()
()()()
()
()()()
()()()
()
()()()
n
n
n
n
n
n
nnnn
xxxxxx
fxfx
xxxxxx
xxxxxx
fx
xxxxxx
xxxxxx
fx
xxxxxx
−
−
−−−
=
−−−
−−−
+
−−−
−−−
++
−−−
(6.77)
Proof Let y=f ( x) be a function which is satisfied
by the (n + 1) points (x
r
, f ( x
r
)), (r= 0, 1, 2 … n)
then
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