## Ward’s “calculus of sequences”, $$q$$-calculus and the limit $$q\to-1$$.(English)Zbl 1111.05010

The author discusses several aspects of $$q$$-calculus, Ward’s calculus of sequences and the connection between them. It is shown that simple additive properties of $$q$$-commuting variables can be understood by “$$q$$-addition”. The limit $$q \rightarrow -1$$ is shown not to be an example of Ward’s calculus. A related work is [M. Schork, J. Phys. A, Math. Gen. 36, No. 16, 4651–4665 (2003; Zbl 1057.81043)].

### MSC:

 05A30 $$q$$-calculus and related topics

### Keywords:

Galois numbers; Gaussian binomial coefficients

Zbl 1057.81043