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GeneralizedPower[f,x,k]

represents Fold[f,Table[x,k]].

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GeneralizedPower

GeneralizedPower[f,x,k]

represents Fold[f,Table[x,k]].

Details

Examples

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Basic Examples  (1)

Represent the third power of NonCommutativeMultiply at x+y:

Wolfram Language code: GeneralizedPower[NonCommutativeMultiply, x + y, 3]

Use NonCommutativeExpand to expand the power of sum:

Wolfram Language code: NonCommutativeExpand[%, NonCommutativeAlgebra[]]

The third GeneralizedPower is equivalent to applying the operation to three copies of the argument:

Wolfram Language code: NonCommutativeExpand[(x + y)**(x + y)**(x + y), NonCommutativeAlgebra[]]

Scope  (5)

Power of a symbolic operation f:

Wolfram Language code: GeneralizedPower[f, g[x, y], 3]

Expand the power over an algebra with product f and vector space addition g:

Wolfram Language code: NonCommutativeExpand[%, NonCommutativeAlgebra[<|"Multiplication" -> f, "Addition" -> g|>]]

GeneralizedPower of Plus and Times autosimplify:

Wolfram Language code: GeneralizedPower[Plus, x, k]
Wolfram Language code: GeneralizedPower[Times, x, k]

Small positive integer GeneralizedPower of numeric functions evaluates at number arguments:

Wolfram Language code: GeneralizedPower[Power, 2, 7]
Wolfram Language code: Fold[Power, Table[2, 7]]

Powers of operations with built-in symbols:

Wolfram Language code: GeneralizedPower[Composition, f, k]
Wolfram Language code: GeneralizedPower[Dot, a, k]
Wolfram Language code: GeneralizedPower[CircleTimes, a, k]

Autosimplification of GeneralizedPower:

Wolfram Language code: f[GeneralizedPower[f, x, k], x]

More general autosimplification for associative (Flat) operations:

Wolfram Language code: SetAttributes[g, Flat]
Wolfram Language code: g[a, x, GeneralizedPower[g, x, k], x, GeneralizedPower[g, x, m], x, b]
Wolfram Language code: GeneralizedPower[g, GeneralizedPower[g, x, k], m]

Properties & Relations  (2)

GeneralizedPower of Times is Power:

Wolfram Language code: GeneralizedPower[Times, x, k]

GeneralizedPower of Plus is Times:

Wolfram Language code: GeneralizedPower[Plus, x, k]
Wolfram Research (2025), GeneralizedPower, Wolfram Language function, https://reference.wolfram.com/language/ref/GeneralizedPower.html.

Text

Wolfram Research (2025), GeneralizedPower, Wolfram Language function, https://reference.wolfram.com/language/ref/GeneralizedPower.html.

CMS

Wolfram Language. 2025. "GeneralizedPower." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/GeneralizedPower.html.

APA

Wolfram Language. (2025). GeneralizedPower. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/GeneralizedPower.html

BibTeX

@misc{reference.wolfram_2026_generalizedpower, author="Wolfram Research", title="{GeneralizedPower}", year="2025", howpublished="\url{https://reference.wolfram.com/language/ref/GeneralizedPower.html}", note=[Accessed: 13-June-2026]}

BibLaTeX

@online{reference.wolfram_2026_generalizedpower, organization={Wolfram Research}, title={GeneralizedPower}, year={2025}, url={https://reference.wolfram.com/language/ref/GeneralizedPower.html}, note=[Accessed: 13-June-2026]}