Frequency of a capacitor and inductor is infinity at initial transient state in a D.C. circuit; is there any mathematical ground to support this.

By initial transient state i mean; the instantaneous state of circuit just after the circuit is closed. Here the circuit mentioned is a D.C. circuit.

At initial transient state we know;

The frequency of a capacitor connected approaches infinity and so the resultant impedance to current flow to due to capacitor is zero and capacitor acts like a short circuit.

Mathematical Relation: Impedance due to capacitor; Z(C)= 1/ (2* pi* frequency* capacitance).

Similarly; the frequency of an inductor is infinity and so the resultant impedance to current flow to due to inductor is infinity and the inductor acts like an open circuit.

Mathematical Relation: Impedance due to inductor; Z(L)= 2* pi* frequency* inductance.

Please correct me wherever i’m wrong :)