Last year my fellow students and I spent a goodly portion of our free time considering the similarities of the relationships between sequences and series and those between derivatives and integrals. During the course of our investigations we deduced a sequence form of the exponential function ex, which stands alone in satisfying the equations
D f = f
f(0) = 1
where D is the differential operator, producing the derivative of the function to which it is applied.
This set us to wondering whether or not we might endeavour to find a discrete analogue of its inverse, the natural logarithmln x , albeit in the sense of being expressed in terms of integers rather than being defined by equations involving sequences and series.
where D is the differential operator, producing the derivative of the function to which it is applied.
This set us to wondering whether or not we might endeavour to find a discrete analogue of its inverse, the natural logarithm
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