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The paper presents an extension µHDC of Higher-order Duration Calculus (HDC, [ZGZ99]) by a polyadic least fixed point (µ) operator and a class of non-logical symbols with a finite variability restriction on their interpretations, which classifies these symbols as intermediate between rigid symbols and flexible symbols as known in DC. The µ operator and the new kind of symbols enable straightforward specification of recursion and data manipulation by HDC. The paper contains a completeness theorem about an extension of the proof system for HDC by axioms about µ and symbols of finite variability for a class of simple µHDC formulas. The completeness theorem is proved by the method of local elimination of the extending operator µ, which was earlier used for a similar purpose in [Gue98].