determine the differential equation satisfied by a polynomial in holonomic functions - Maple Help

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gfun[poltodiffeq] - determine the differential equation satisfied by a polynomial in holonomic functions

Calling Sequence

poltodiffeq(P, listdiffeq, list_unknowns, y(z))

Parameters

P

-

polynomial in z and y1(z), y2(z), ... and possibly their derivatives and repeated derivatives

listdiffeq

-

list containing, for each of y1(z), y2(z), ..., either a linear differential equation it satisfies or a set containing the equation together with initial conditions

list_unknowns

-

list of function names [y1z,y2z,...] 

y

-

name; holonomic function name

z

-

name; variable of the holonomic function y

Description

• 

The poltodiffeq(P, listdiffeq, list_unknowns, y(z)) command returns a linear differential equation satisfied by the polynomial P.

  

If y1(z), y2(z), ... are holonomic function solutions of listdiffeq[1], listdiffeq[2], ..., the poltodiffeq function returns a linear differential equation satisfied by Pz,y1z,....

Examples

withgfun:

Sin:=ⅆ2ⅆz2y1z=y1z,y10=0,Dy10=1:

Cos:=ⅆ2ⅆz2y2z=y2z,y20=1,Dy20=0:

poltodiffeqy1z2+y2z2,Sin,Cos,y1z,y2z,yz

ⅆ3ⅆz3yz+4ⅆⅆzyz,y0=1,Dy0=0,D2y0=0

(1)

poltodiffeqy1z2+ⅆⅆzy1z2,Sin,y1z,yz

ⅆⅆzyz,y0=1

(2)

See Also

gfun, gfun[`diffeq+diffeq`], gfun[`diffeq*diffeq`], gfun[parameters], gfun[poltorec]


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