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gfun

  

listtoratpoly

  

find a rational generating function

  

seriestoratpoly

  

find a rational approximation

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

listtoratpoly(l, x, [typelist])

seriestoratpoly(s, [typelist])

Parameters

l

-

list

x

-

name; variable name

typelist

-

(optional) list of generating function types. The default is 'ogf','egf'. For a complete list of types, see gftypes.

s

-

series

Description

• 

The listtoratpoly(l, x, [typelist]) command computes a rational function in x for the generating function of the expressions in l.  This generating function is one of the types specified by typelist, for example, ordinary (ogf) or exponential (egf). For a complete list of available generating function types, see gftypes.

  

You should specify as many terms as possible in the list l.

• 

The seriestoratpoly(s, x, [typelist]) command computes a rational function in x for the generating function of the expressions in s.  This generating function is one of the types specified by typelist, for example, ordinary (ogf) or exponential (egf). For a complete list of available generating function types, see gftypes.

  

You should specify as many terms as possible in the series s.

• 

If typelist contains more than one element, these types are considered in the order that they are listed.

• 

If typelist is not specified, the default typelist, 'ogf','egf' is used.

  

The function returns a list whose first element is the rational function. The second element is the generating function type for which a solution was found.

• 

These functions are frontends to convert[ratpoly] which performs the actual computation.

Examples

If the input is the first few elements of the Fibonacci sequence, the function returns the generating series for the Fibonacci numbers.

withgfun:

l1,1,2,3,5,8,13

l:=1,1,2,3,5,8,13

(1)

listtoratpolyl,x

1x2+x1,ogf

(2)

seriestoratpolyseries1+x+2x22!+3x33!+5x44!+8x55!+13x66!,x,8,'egf'

1x2+x1,egf

(3)

See Also

convert[ratpoly]

gfun

gfun/gftypes

gfun/parameters

 


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