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Taylor expansion definition of the exponential function
Ciro Santilli
(
@cirosantilli,
37
)
...
Function (mathematics)
Function by signature
Numeric function
Exponentiation
Exponential function
Definition of the exponential function
Updated
2025-07-16
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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)
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(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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