Wikidata:Property proposal/power series expansion

power series expansion

Originally proposed at Wikidata:Property proposal/Natural science

   Done: power series expansion (P10969) (Talk and documentation)

Description	The power series expansion of the subject.
Represents	power series (Q206925)
Data type	Mathematical expression
Example 1	exponential function (Q168698) → $e^{x}=1+x+{\frac {x^{2}}{2}}+{\frac {x^{3}}{6}}+\cdots +{\frac {x^{n}}{n!}}+\cdots$
Example 2	sine (Q152415) → $\sin x=x-{\frac {x^{3}}{3!}}+{\frac {x^{5}}{5!}}-\ldots$
Example 3	Lambert W function (Q429331) → $W_{0}(x)=\sum _{n=1}^{\infty }{\frac {(-n)^{n-1}}{n!}}x^{n}=x-x^{2}+{\tfrac {3}{2}}x^{3}-{\tfrac {8}{3}}x^{4}+{\tfrac {125}{24}}x^{5}-\cdots$
Expected completeness	eventually complete (Q21873974)
See also	defining formula (P2534)
Wikidata project	WikiProject Mathematics (Q8487137)

Motivation

Taylor and Laurent series expansions are important properties of mathematics. Currently they are missing. Midleading (talk) 08:00, 10 August 2022 (UTC)

Discussion

•  Support This would be good to have. Note power series are not necessarily expanded about x = 0 (powers of x) - for example you can't do that for natural logarithm (Q204037) - have you considered whether qualifiers or some other mechanism would be needed in those cases? ArthurPSmith (talk) 18:34, 11 August 2022 (UTC)

Required qualifiers include center of power series expansion, region of convergence. However none have suitable existing properties. Therefore they have to be recorded in the mathematical expression in a human-readable way. $\ln(1+x)=\sum _{k=1}^{\infty }{\frac {(-1)^{k-1}}{k}}x^{k}=x-{\frac {x^{2}}{2}}+{\frac {x^{3}}{3}}-\cdots$ --Midleading (talk) 04:10, 12 August 2022 (UTC)

•  Support Midleading's clarification aboce is important, though; not all expansions are around zero. The Anome (talk) 20:44, 15 August 2022 (UTC)
•  Support --Tinker Bell ★ ♥ 04:46, 16 August 2022 (UTC)

@Midleading, ArthurPSmith, The Anome, Tinker Bell:  Done Now power series expansion (P10969). --Lymantria (talk) 06:15, 23 August 2022 (UTC)