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Definition df-em 25071
Description: Define the Euler-Mascheroni constant, γ = 0.577.... This is the limit of the series Σ𝑘 ∈ (1...𝑚)(1 / 𝑘) − (log‘𝑚), with a proof that the limit exists in emcl 25081. (Contributed by Mario Carneiro, 11-Jul-2014.)
Assertion
Ref Expression
df-em γ = Σ𝑘 ∈ ℕ ((1 / 𝑘) − (log‘(1 + (1 / 𝑘))))

Detailed syntax breakdown of Definition df-em
StepHypRef Expression
1 cem 25070 . 2 class γ
2 cn 11312 . . 3 class
3 c1 10225 . . . . 5 class 1
4 vk . . . . . 6 setvar 𝑘
54cv 1652 . . . . 5 class 𝑘
6 cdiv 10976 . . . . 5 class /
73, 5, 6co 6878 . . . 4 class (1 / 𝑘)
8 caddc 10227 . . . . . 6 class +
93, 7, 8co 6878 . . . . 5 class (1 + (1 / 𝑘))
10 clog 24642 . . . . 5 class log
119, 10cfv 6101 . . . 4 class (log‘(1 + (1 / 𝑘)))
12 cmin 10556 . . . 4 class
137, 11, 12co 6878 . . 3 class ((1 / 𝑘) − (log‘(1 + (1 / 𝑘))))
142, 13, 4csu 14757 . 2 class Σ𝑘 ∈ ℕ ((1 / 𝑘) − (log‘(1 + (1 / 𝑘))))
151, 14wceq 1653 1 wff γ = Σ𝑘 ∈ ℕ ((1 / 𝑘) − (log‘(1 + (1 / 𝑘))))
Colors of variables: wff setvar class
This definition is referenced by:  emcllem6  25079
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