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Definition df-ef 15417
 Description: Define the exponential function. Its value at the complex number 𝐴 is (exp‘𝐴) and is called the "exponential of 𝐴"; see efval 15429. (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 15411 . 2 class exp
2 vx . . 3 setvar 𝑥
3 cc 10528 . . 3 class
4 cn0 11889 . . . 4 class 0
52cv 1537 . . . . . 6 class 𝑥
6 vk . . . . . . 7 setvar 𝑘
76cv 1537 . . . . . 6 class 𝑘
8 cexp 13429 . . . . . 6 class
95, 7, 8co 7139 . . . . 5 class (𝑥𝑘)
10 cfa 13633 . . . . . 6 class !
117, 10cfv 6328 . . . . 5 class (!‘𝑘)
12 cdiv 11290 . . . . 5 class /
139, 11, 12co 7139 . . . 4 class ((𝑥𝑘) / (!‘𝑘))
144, 13, 6csu 15038 . . 3 class Σ𝑘 ∈ ℕ0 ((𝑥𝑘) / (!‘𝑘))
152, 3, 14cmpt 5113 . 2 class (𝑥 ∈ ℂ ↦ Σ𝑘 ∈ ℕ0 ((𝑥𝑘) / (!‘𝑘)))
161, 15wceq 1538 1 wff exp = (𝑥 ∈ ℂ ↦ Σ𝑘 ∈ ℕ0 ((𝑥𝑘) / (!‘𝑘)))
 Colors of variables: wff setvar class This definition is referenced by:  efval  15429  eff  15431
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