# Is self-inductance and velocity factor included in equations for half wave dipole imdedance?

Can anyone tell me if the equations below for the impedance at the center feed points of a half wave dipole include terms for self inductance and velocity factor of the elements, and if so provide an explanation ?

A dipole half wave in length has + 45 ohms of reactance in the feed point impedance, i'm trying to figure out exactly what causes this reactance.

If the equations assume no self inductance and a velocity factor of 1, what causes the reactance ?

The impedance formula you quoted assumes that the radiator is made of an ideal cylindrical conductor, ie., completely lossless idealized material that is represented by the boundary conditions: $$n\cdot H=0$$ and $$n\times E=0$$. Whatever low frequency inductance and/or capacitance it may have as a pair of metal pieces is already built in the formula.
It has a reactance because the pair of cylinders do not have a constant wave impedance as a pair of transmission lines (imagine you are pushing the far ends of parallel wires apart while keeping their feed points together) and also because the vacuum impedance ($$377\Omega$$) is not a proper termination at the far ends.
If by including the "velocity factor" you mean whether the formula would work for an antenna embedded in a homogeneous and lossless linear dielectric medium or some such then the answer is yes, $$k=2\pi\sqrt {\mu_r \epsilon_r}/\lambda_0$$, and $$\lambda_0$$ is the free-space wavelength.