Analytic solution of this recurrence equation in complex Z-plane?
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From: mike3 on 16 May 2010 22:52 Hi. Can one find an analytic solution to the recurrence functional equation F(z+1) = z F(z) + 2 F(z-1) - (z-4) F(z-2) - F(z-3) F(0) = 1, F(1) = 0, F(2) = 0, F(3) = 1 in the complex z-plane? Can such a solution be expressed in closed form using generally-accepted mathematical special functions, even if it is not elementary? Perhaps with some kind of hypergeometric or related thing? If such a thing is not possible, how about a Taylor series but with explicit formulas for the coefficients?
From: mike3 on 16 May 2010 23:30
On May 16, 8:52 pm, mike3 <mike4...(a)yahoo.com> wrote: > Hi. > > Can one find an analytic solution to the recurrence functional > equation > > F(z+1) = z F(z) + 2 F(z-1) - (z-4) F(z-2) - F(z-3) > F(0) = 1, F(1) = 0, F(2) = 0, F(3) = 1 > > in the complex z-plane? Can such a solution be expressed in closed > form using generally-accepted mathematical special functions, even if > it is not elementary? Perhaps with some kind of hypergeometric or > related thing? If such a thing is not possible, how about a Taylor > series but with explicit formulas for the coefficients? Oops, I got the wrong initial conditions. It should be F(0) = 2, F(1) = -1, F(2) = 0, F(3) = 1. |