Building on the work which will appear in my thesis and certain formalism introduced in F. Pellarin's paper \textit{Values of certain $L$-series in positive characteristic}, I will introduce a family arising from the Carlitz module in the ring of twisted power series over the ring $K$ of rational functions in one indeterminate with coefficients in a finite field. I will describe how this family gives rise to both the explicit calculation of the rational functions appearing (inexplicitly) in Pellarin's main result in the paper above and also to certain $K$-relations between Thakur's multizeta values originally introduced in his book \textit{Function Field Arithmetic}. This is a joint work with F. Pellarin.