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by
Ciro Santilli
(
@cirosantilli,
36
)
Taylor expansion definition of the exponential function
...
Function (mathematics)
Function by signature
Numeric function
Exponentiation
Exponential function
Definition of the exponential function
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Updated
2025-04-24
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Created
1970-01-01
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The
Taylor series
expansion is the most direct
definition
of the expontial
as
it obviously satisfies the
exponential function differential equation
:
the
first
constant term
dies
each other term gets converted to the one before
because
we
have
infinite
many terms,
we
get what
we
started with!
e
x
=
∑
n
=
0
∞
n
!
x
n
=
1
+
1
x
+
2
x
2
+
2
×
3
x
3
+
2
×
3
×
4
x
4
+
…
(1)
Ancestors
(10)
Definition of the exponential function
Exponential function
Exponentiation
Numeric function
Function by signature
Function (mathematics)
Formalization of mathematics
Area of mathematics
Mathematics
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Exponential map (Lie theory)
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