Below are well known equations from Wikipedia for the resistance and reactance in the impedance of a dipole antenna. 

[![enter image description here][1]][1]

  [1]: https://i.sstatic.net/GYTV0.png

where a is the radius of the conductors, k is the wave number 2πf/c, η0 denotes the impedance of free space = 377Ω, and γe is Euler's constant = 0.57721566. 

Wikipedia doesn't specify where the feed point is, but since the feed point impedance is a function of the position of the feed point along the antenna, and there are no variable terms in the equations for feed point position, i assume the equations are for a feed point in the center.

Notice how there are no terms anywhere in the equations for anything related to the self inductance of the elements, or related to the fact that radio waves travel slower in metal than in air. 

Every one knows that a center fed dipole exactly 1/2 λ in length has about + 45 Ω of reactance at the feed point impedance so to make it resonant it has to be shortened about 5 %. 

I proved this by writing a program using Microsoft Visual Studio .NET which allows me to input different values for frequency, length and radius and which then calculates R and X using these equations. The program showed that a dipole which is exactly 1/2 λ in length does in fact have + 45 Ω of reactance in the feed point impedance.

I seems undeniable that the presence of self inductance in the elements of a dipole will affect the reactance in the feed point impedance, and similarly the velocity factor of the metal will affect the resonant length and so also affect the feed point reactance, so it seems strange that the above equation for reactance doesn't include terms for these factors. 

In order to be resonant, a dipole must have to be shortened also to allow for self inductance of the elements and for the fact that the radio waves travel slower in the elements than in air, right ?

So considering the above equations, does the self inductance and velocity factor of the elements of a dipole change it's resonant frequency ?