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power series expansion
power series expansion of the subject
In more languages
Data type
Mathematical expression
Statements
instance of
Wikidata property related to mathematics
0 references
maintained by WikiProject
WikiProject Mathematics
0 references
Wikidata item of this property
power series expansion
0 references
Wikidata property example
exponential function
power series expansion
e
x
=
∑
n
=
0
∞
x
n
n
!
=
1
+
x
+
x
2
2
!
+
x
3
3
!
+
⋯
+
x
n
n
!
+
⋯
{\displaystyle 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 }
0 references
sine
power series expansion
sin
(
x
)
=
∑
n
=
0
∞
(
−
1
)
n
x
2
n
+
1
(
2
n
+
1
)
!
=
x
−
x
3
3
!
+
x
5
5
!
−
…
{\displaystyle \sin(x)=\sum _{n=0}^{\infty }{\frac {(-1)^{n}x^{2n+1}}{(2n+1)!}}=x-{\frac {x^{3}}{3!}}+{\frac {x^{5}}{5!}}-\ldots }
0 references
Lambert W function
power series expansion
W
0
(
x
)
=
∑
n
=
1
∞
(
−
n
)
n
−
1
n
!
x
n
=
x
−
x
2
+
3
2
x
3
−
8
3
x
4
+
125
24
x
5
−
…
{\displaystyle 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
)
=
∑
k
=
1
∞
(
−
1
)
k
−
1
k
x
k
=
x
−
x
2
2
+
x
3
3
−
⋯
{\displaystyle \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
property scope
as main value
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allowed-entity-types constraint
item of property constraint
Wikibase item
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