gfun
poltodiffeq
determine the differential equation satisfied by a polynomial in holonomic functions
Calling Sequence
Parameters
Description
Examples
poltodiffeq(P, listdiffeq, list_unknowns, y(z))
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
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,....
withgfun:
Sin≔diffy1z,z,z=−y1z,y10=0,Dy10=1:
Cos≔diffy2z,z,z=−y2z,y20=1,Dy20=0:
poltodiffeqy1z2+y2z2,Sin,Cos,y1z,y2z,yz
ⅆ3ⅆz3yz+4ⅆⅆzyz,y0=1,Dy0=0,D2y0=0
poltodiffeqy1z2+diffy1z,z2,Sin,y1z,yz
ⅆⅆzyz,y0=1
See Also
gfun[`diffeq+diffeq`]
gfun[`diffeq*diffeq`]
gfun[parameters]
gfun[poltorec]
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