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gfun[borel] - compute the Borel transform of a generating function
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
The invborel command is the inverse command.
You can also perform Borel transforms on the corresponding differential equations.
See Also
gfun, gfun[diffeqtorec], gfun[invborel], rectodiffeq
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