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Key Equations
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Aa
Key Equations
Power series centered at
x
=
0
x
=
0
∑
n
=
0
∞
c
n
x
n
=
c
0
+
c
1
x
+
c
2
x
2
+
⋯
∑
n
=
0
∞
c
n
x
n
=
c
0
+
c
1
x
+
c
2
x
2
+
⋯
Power series centered at
x
=
a
x
=
a
∑
n
=
0
∞
c
n
(
x
−
a
)
n
=
c
0
+
c
1
(
x
−
a
)
+
c
2
(
x
−
a
)
2
+
⋯
∑
n
=
0
∞
c
n
(
x
−
a
)
n
=
c
0
+
c
1
(
x
−
a
)
+
c
2
(
x
−
a
)
2
+
⋯
Taylor series for the function
f
f
at the point
x
=
a
x
=
a
∑
n
=
0
∞
f
(
n
)
(
a
)
n
!
(
x
−
a
)
n
=
f
(
a
)
+
f
′
(
a
)
(
x
−
a
)
+
f
″
(
a
)
2
!
(
x
−
a
)
2
+
⋯
+
f
(
n
)
(
a
)
n
!
(
x
−
a
)
n
+
⋯
∑
n
=
0
∞
f
(
n
)
(
a
)
n
!
(
x
−
a
)
n
=
f
(
a
)
+
f
′
(
a
)
(
x
−
a
)
+
f
″
(
a
)
2
!
(
x
−
a
)
2
+
⋯
+
f
(
n
)
(
a
)
n
!
(
x
−
a
)
n
+
⋯
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