power series expansion (P10969)

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power series expansion of the subject

Language	Label	Description	Also known as
English	power series expansion	power series expansion of the subject

Data type

Mathematical expression

Statements

Wikidata property related to mathematics

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maintained by WikiProject

WikiProject Mathematics

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Wikidata item of this property

power series expansion

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Wikidata property example

exponential function

power series expansion

e^{x}=\sum _{n=0}^{\infty }{\frac {x^{n}}{n!}}=1+x+{\frac {x^{2}}{2!}}+{\frac {x^{3}}{3!}}+\cdots +{\frac {x^{n}}{n!}}+\cdots

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power series expansion

\sin(x)=\sum _{n=0}^{\infty }{\frac {(-1)^{n}x^{2n+1}}{(2n+1)!}}=x-{\frac {x^{3}}{3!}}+{\frac {x^{5}}{5!}}-\ldots

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Lambert W function

power series expansion

W_{0}(x)=\sum _{n=1}^{\infty }{\frac {(-n)^{n-1}}{n!}}x^{n}=x-x^{2}+{\tfrac {3}{2}}x^{3}-{\tfrac {8}{3}}x^{4}+{\tfrac {125}{24}}x^{5}-\ldots

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natural logarithm

power series expansion

\ln(1+x)=\sum _{k=1}^{\infty }{\frac {(-1)^{k-1}}{k}}x^{k}=x-{\frac {x^{2}}{2}}+{\frac {x^{3}}{3}}-\cdots

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expected completeness

eventually complete

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property proposal discussion

https://www.wikidata.org/wiki/Wikidata:Property_proposal/power_series_expansion

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Constraints

property constraint

property scope constraint

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allowed-entity-types constraint

item of property constraint

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