convert a linear differential equation into a recurrence
diffeqtorec(deq, y(z), u(n))
linear differential equation in y(z) with polynomial coefficients
name; function name
name; variable of the function y
name; recurrence name
name; index of the recurrence u
The diffeqtorec(deq, y(z), u(n)) command converts a linear differential equation, deq, into a recurrence.
Let f be a power series solution of the differential equation.
If u(n) is the nth Taylor coefficient of f around zero, the diffeqtorec function returns a linear recurrence for the numbers u(n), with rational coefficients in n.
The syntax is the same as that of dsolve. Combined with algeqtodiffeq, this function produces a linear recurrence for the Taylor coefficients of an algebraic function.
deq ≔ algeqtodiffeq⁡y=1+z⁢y2+y3,y⁡z,:
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