... q)-analogs of the tangent and secant numbers, respectively They may be regarded as the graded forms of the traditional q -tangent and q -secant numbers T2n+1 (q), En (q) defined in (1.1)q and (1.2)q ... thoroughly studied and n used in our previous paper [FH08] However, the extensions T2n+1 (t, q) and E2n (t, q) the electronic journal of combinatorics 18(2) (2011), #P7 of tangent and secant, as true ... q sin(r) (u) q (r) ; (r) ; cosq (u) cosq (u) and define the (t, q)-analogs of the tangent and secant numbers as being the coefficients T2n+1 (t, q) and E2n (t, q), respectively, in the following...