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Numerical Methods/The Calculus of finite differences / Relation In Forward Backward, Shift Operator
1.Δ {f(x)g(x)} = f(x+h)Δg(x) + g(x)Δf(x) Example. Δ( e^ax log bx) 2.Δ { f(x) / g(x) } = [ g(x) Δf(x) - f(x) Δg(x) ] / g(x+h) g(x) 3.Δ,∇ and E operators are not commutative . 4.Δ,∇ and E operators can not stand without two operand . Relations between the operators Δ, ∇ and E: 1. Δ ≡ E −1 2. Δ E ≡ Δ E 3. ∇≡ E −1 / E ...
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