# Delta formal definition for DFA

How can I formally define 𝛿* for a dfa with multiple initial states? I know that the δ formal definition for NFA is δ: Q × ∑ → 2^Q and for DFA it's δ : Q × Σ → Q but what should I do if there is multiple initial states?How can I take into consideration all the options for the initial state?It seem like it should combine the NFA definition and DFA definition.. δ: 2^Q × ∑ → Q maybe?but it doesn't seem right neither.

I would appreciate any help I can get on this matter