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...Electronic journal of dierential equations vol no pp issn url http ejde math txstate edu or unt extending putzer s representation to all analytic matrix functions via omega calculus antoniofrancisconeto abstract weshowthatputzer smethodtocalculatethematrixexponential in can be generalized compute an arbitrary function dened by a convergent power series the main technical tool for adapting formulation general setting is that extension macmahon partition analysis realm and method several results literature are shown special cases our formalism including computation fractional exponentials introduced rodrigo much more direct conceptually simple computing approach recursive system base explicitly solved we need determine introduction let t cn with n then solution initial value problem exp ta where exponential x k which valued any terms constructed avoiding use jordan canonical form requiring not theknowledgeoftheeigenvaluesofa smethodhasthenice feature being generic it holds square even re...