We introduce a fourth operator 1 called the identity
operator, which is defined by
1f
x
=f
x
(6.31)
6.3.3 The Relations Between
D, —, E and 1
Since
D f
x
=f
x+h
−f
x
=E. f
x
− 1. f
x
or
Ef
x
= 1f
x
+D f
x
= (1 +D)f
x
(6.32)
Thus, E and 1 +D when applied on a function f
x
produce the same result. Hence, they may be treated
as equivalent operators:
E= 1 +D (6.33)
Note ...
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