12 Generating Functions - MIT OpenCourseWare
What happens if we take the derivative of a generating function? As an exam-ple, let’s differentiate the now-familiar generating function for an infinite sequence of 1’s: 1CxCx2Cx3Cx4CD 1 1 x IMPLIES d dx.1CxCx2Cx3Cx4C /D d dx 1 1 x IMPLIES 1C2xC3x2C4x3CD 1.1 x/2 IMPLIES h1;2;3;4;:::i ! 1.1 x/2: (12.1)
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