Parallel connections and coloured Tutte polynomials

We give formulas for the Tutte polynomials of parallel and series connections of weighted matroids, generalizing and unifying formulas of Oxley and Welsh (Discrete Math. 109 (1992) 185), Bollobás and Riordan (Comb. Probab. Comput. 8 (1999) 45) and Woodall (Discrete Math. 247 (2002) 201).