We know that there exists similarities between power functions and derivative of a function (in particular, Newton binomial formula and Leibniz rule for derivation of a product can be deduced from each other). Thanks to the alternant formula, we can express the determinant of a Vandermonde matrix with a missing power (e.g. see [this post](https://math.stackexchange.com/questions/3024496/computing-an-almost-vandermonde-matrix)) via a power function of its coefficients.


**Question**: Does it exist a similar formula for the Wronskian of arbitrary functions :

$$
W_k(f_1,\ldots, f_{n}) = 
\begin{vmatrix}
f_1&\ldots&f_1^{(k-1)}&f_1^{(k+1)}&\ldots &f_1^{(n)}\\
\vdots & \ddots & \vdots & \vdots & \ddots & \vdots \\ 
f_n&\ldots&f_n^{(k-1)}&f_n^{(k+1)}&\ldots &f_n^{(n)}
\end{vmatrix}
$$