({{, (RefLink[FunctionSpace, paclet:ref/FunctionSpace]) 
is an option for (RefLink[FindSequenceFunction, paclet:ref/FindSequenceFunction]) and related functions that specifies the space of functions to consider for representations. }})

OpenersNotesSection(Spacer1)Details

With an explicit setting for (RefLink[FunctionSpace, paclet:ref/FunctionSpace])->s, only functions of type s will be considered.

(RefLink[FunctionSpace, paclet:ref/FunctionSpace])->{(Subscript[s, 1]),(Subscript[s, 2]),…} specifies that types (Subscript[s, 1]), (Subscript[s, 2]), … should be considered.

(RefLink[FunctionSpace, paclet:ref/FunctionSpace])->(RefLink[All, paclet:ref/All]) uses all available types.

Possible types of discrete functions include:

Possible types of continuous functions include:

OpenersPrimaryExamplesSection(Spacer1)Examples  (1)

OpenersExampleSection0(Spacer1)Basic Examples  (1)

By default, a small generating function is found if possible:

FindGeneratingFunction[Table[2^n,{n,0,10}],x]

SeriesCoefficient[%,{x,0,n}]

Use (RefLink[FunctionSpace, paclet:ref/FunctionSpace]) to control the forms found:

FindGeneratingFunction[Table[2^n,{n,0,10}],x,FunctionSpace->"Polynomial"]

({{DocumentationFooterIconsRelatedFunction.png, ({{See Also}, {(RefLink[ValidationLength, paclet:ref/ValidationLength])  ▪  (RefLink[FindGeneratingFunction, paclet:ref/FindGeneratingFunction])  ▪  (RefLink[FindSequenceFunction, paclet:ref/FindSequenceFunction])}})}})