Re: [math-fun] discrete version of exp(d/dz)
27 Dec
2009
27 Dec
'09
4:56 p.m.
Mike Stay writes: << It's straightforward to show that exp(d/dz)f(z) = f(z+1). . . . . . .
I'll just point out this holds for functions f defined by a convergent power series, but not necessarily for those that are not. E.g., the famous example f: R -> R via f(x) = exp(-1/x^2), x <> 0 and f(0) = 0 has exp(d/dx)f(x) = 1 at x = 0 but f(0+1) = f(1) = 1/e. --Dan _____________________________________________________________________ "It don't mean a thing if it ain't got that certain je ne sais quoi." --Peter Schickele
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Dan Asimov