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Definition df-ef 11103
 Description: Define the exponential function. Its value at the complex number 𝐴 is (exp‘𝐴) and is called the "exponential of 𝐴"; see efval 11116. (Contributed by NM, 14-Mar-2005.)
Assertion
Ref Expression
df-ef exp = (𝑥 ∈ ℂ ↦ Σ𝑘 ∈ ℕ0 ((𝑥𝑘) / (!‘𝑘)))
Distinct variable group:   𝑥,𝑘

Detailed syntax breakdown of Definition df-ef
StepHypRef Expression
1 ce 11097 . 2 class exp
2 vx . . 3 setvar 𝑥
3 cc 7445 . . 3 class
4 cn0 8771 . . . 4 class 0
52cv 1295 . . . . . 6 class 𝑥
6 vk . . . . . . 7 setvar 𝑘
76cv 1295 . . . . . 6 class 𝑘
8 cexp 10085 . . . . . 6 class
95, 7, 8co 5690 . . . . 5 class (𝑥𝑘)
10 cfa 10264 . . . . . 6 class !
117, 10cfv 5049 . . . . 5 class (!‘𝑘)
12 cdiv 8236 . . . . 5 class /
139, 11, 12co 5690 . . . 4 class ((𝑥𝑘) / (!‘𝑘))
144, 13, 6csu 10912 . . 3 class Σ𝑘 ∈ ℕ0 ((𝑥𝑘) / (!‘𝑘))
152, 3, 14cmpt 3921 . 2 class (𝑥 ∈ ℂ ↦ Σ𝑘 ∈ ℕ0 ((𝑥𝑘) / (!‘𝑘)))
161, 15wceq 1296 1 wff exp = (𝑥 ∈ ℂ ↦ Σ𝑘 ∈ ℕ0 ((𝑥𝑘) / (!‘𝑘)))
 Colors of variables: wff set class This definition is referenced by:  efval  11116  eff  11118
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