borel - Maple Help
For the best experience, we recommend viewing online help using Google Chrome or Microsoft Edge.

Online Help

All Products    Maple    MapleSim


gfun

  

borel

  

compute the Borel transform of a generating function

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

borel(expr, a(n), t)

Parameters

expr

-

linear recurrence with polynomial coefficients

a

-

name; recurrence name

n

-

name; index of the recurrence a

t

-

(optional) 'diffeq'; specify as a linear differential equation

Description

• 

The borel(expr, a(n)) command computes the Borel transform of a generating function.

• 

If  is the sequence of numbers defined by the recurrence expr, the borel function computes the recurrence for the numbers .

• 

If  is the sequence of numbers defined by the recurrence expr, the procedure computes the recurrence for the numbers .

• 

If t is specified as 'diffeq', expr is considered as a linear differential equation with polynomial coefficients for the function . In this case, the function returns a linear differential equation satisfied by the Borel transform of .

Examples

(1)

The invborel command is the inverse command.

(2)

You can also perform Borel transforms on the corresponding differential equations.

(3)

(4)

See Also

gfun

gfun[diffeqtorec]

gfun[invborel]

rectodiffeq

 


Download Help Document