expq
Expq, often written as exp_q(x), is a family of q-analogues of the exponential function used in q-calculus, combinatorics, and mathematical physics. The precise form and notation vary by author, but the core idea is to generalize the ordinary exponential with a deformation parameter q. In most treatments, exp_q reduces to the standard exponential e^x when q tends to 1.
A common definition uses the q-integers [n]_q and the q-factorial [n]_q!: [n]_q = (1 - q^n)/(1 - q) and
Properties of exp_q include analyticity near x = 0 and the satisfaction of q-difference equations rather than
Applications of exp_q appear across q-calculus, quantum groups, and combinatorics. It appears in generating functions, deformations