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Prove-x-m-p-n-n-m-p-n-n-p-n-x-n-c-p-n-




Question Number 216661 by MrGaster last updated on 14/Feb/25
Prove:⟨x^m ⟩=Σ_({p_n }) ^� Π^n ((m!)/(p_n !(n!)^p_n  ))⟨x^n ⟩_c ^p_n
$$\mathrm{Prove}:\langle{x}^{{m}} \rangle=\underset{\left\{{p}_{{n}} \right\}} {\acute {\sum}}\overset{{n}} {\prod}\frac{{m}!}{{p}_{{n}} !\left({n}!\right)^{{p}_{{n}} } }\langle{x}^{{n}} \rangle_{{c}} ^{{p}_{{n}} } \\ $$

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