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gfun

  

holexprtodiffeq

  

produce a differential equation satisfied by a holonomic expression

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

holexprtodiffeq(expr, y(z))

Parameters

expr

-

holonomic expression in y(z)

y

-

name; holonomic function name

z

-

name; variable of the holonomic function y

Description

• 

The gfun[holexprtodiffeq](expr, y(z)) command produces a differential equation satisfied by the holonomic expression expr.

  

If expr is a holonomic expression, then the gfun[holexprtodiffeq] function returns a differential equation in y and z that is satisfied by expr. Initial conditions are returned when possible.

• 

Not all holonomic functions are recognized by holexprtodiffeq. It currently accepts the following functions.

 

 

 

 

 

 

BesselI

BesselJ

BesselK

BesselY

arccos

arccosh

arccot

arccoth

arccsc

arccsch

arcsec

arcsech

arcsin

arcsinh

arctan

arctanh

cos

cosh

erf

erfc

exp

ln

sin

sinh

 

 

 

 

 

 

Examples

withgfun:

holexprtodiffeqBesselJ2,x,yx

x2ⅆ2ⅆx2yx+xⅆⅆxyx+x24yx,D2y0=14

(1)

holexprtodiffeqarcsec1x+sinx2,yx

16x58x3+52xⅆⅆxyx+16x640x4+44x220ⅆ2ⅆx2yx+4x52x3+13xⅆ3ⅆx3yx+4x610x4+11x25ⅆ4ⅆx4yx,y0=12π,Dy0=1,D2y0=2,D3y0=1

(2)

See Also

BesselJ

gfun

gfun[diffeqtohomdiffeq]

gfun[diffeqtorec]

 


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