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This article introduces an algebra of functions in one variable $c$ definedby iterated integrals of two specific differential forms depending on $c$,where the product is the shuffle product. This algebra can be seen as a commondeformation of multiple zeta values and of Kaneko-Tsumura's recent multiple$T$-values. The first few graded dimensions, assuming that a grading by theweight does hold, are computed.

Multiple $T$-values with one parameter