Thus a dual Grothendieck polynomial is still a discrete Wronskian
that one identifies with a multiSchur function (in the case of an increasing or decreasing sequence of alphabets, one also uses the term flagged Schur function cf.
where <y, z> := yz' - y'z is the Wronskian
of y and z.
If X, Y [member of] D, then we define the Wronskian
matrix of X(t) and Y(t) by
21) ensures that the Wronskian
matrix of the linearly independent functions ([v.
are linearly independent by computing its Wronskian
at t = 0.
W is the Wronskian
of the two independent solutions, which is constant, being the layer matrix M unimodular, and:
4) are linearly independent if and only if their Wronskian
is different from zero.
i] are linearly independent over F, then there exists a generalized Wronskian
of the (3), which does not vanish.
The accuracy of the results can be checked using the Wronskians
for Mathieu functions, as the algorithms for computing Mathieu functions are not based on the Wronskian
of the functions.
Since the Wronskian
of any two solution of (8) is independent of t, while t [right arrow] [infinity] in (11) we also get
Marini, On intermediate solutions and the Wronskian
for half-linear differential equations, J.
This generalization is obtained by considering the Wronskian
of functions over F[x].