Physics · Mathematical Physics
Which of the following identities is NOT true regarding the Dirac delta function δ(x) and its nth derivative δ(n)(x)?
- 1xmδ(n)(x) = (-1)n n!(n - m)! δ(n - m)(x) if m ≤ n✓
- 2xmδ(n)(x) = (-1)m n!(n - m)! δ(n - m)(x) if m ≤ n
- 3xmδ(n)(x) = (-1)n n!δ(x) if m = n
- 4xmδ(n)(x) = 0 if m > n
Correct answer
xmδ(n)(x) = (-1)n n!(n - m)! δ(n - m)(x) if m ≤ n
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