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gfun

  

diffeqtorec

  

convert a linear differential equation into a recurrence

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

diffeqtorec(deq, y(z), u(n))

Parameters

deq

-

linear differential equation in y(z) with polynomial coefficients

y

-

name; function name

z

-

name; variable of the function y

u

-

name; recurrence name

n

-

name; index of the recurrence u

Description

• 

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.

Examples

withgfun:

diffeqtorecyz=aⅆⅆzyz,yz,vn

vn+anavn+1

(1)

deqalgeqtodiffeqy=1+zy2+y3,yz,:

diffeqtorecdeq,yz,um

2m2mum+18m230m9um+1+46m2+227m+279um+2+4m226m42um+3,u0=1,u1=2,u2=10

(2)

See Also

dsolve

dsolve/formal_series

gfun

gfun[algeqtodiffeq]

gfun[rectodiffeq]

 


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