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density function is f ( x ) = 1 σ 2 π e − 1 2 ( x − μ σ ) 2 {\displaystyle f(x)={\frac {1}{\sigma {\sqrt {2\pi }}}}e^{-{\frac {1}{2}}\left({\frac {x-\mu...

variable, μ (mu) is the mean of the distribution, and σ (sigma) is its standard deviation: Pr ( μ − 1 σ ≤ X ≤ μ + 1 σ ) ≈ 68.27 % Pr ( μ − 2 σ ≤ X ≤ μ + 2 σ...

) = μ ( m n ) + ∑ d | m n ; d < m n μ ( d ) = induction μ ( m n ) − μ ( m ) μ ( n ) + ∑ d | m ; d ′ | n μ ( d ) μ ( d ′ ) = μ ( m n ) − μ ( m ) μ ( n...

distinct prime factors. For the latter μ ( n ) = ( − 1 ) 2 x = 1 {\displaystyle \mu (n)=(-1)^{2x}=1} (where μ is the Möbius function and x is half the...

sum of its primitive roots is congruent to μ(p − 1) modulo p, where μ is the Möbius function. For example, E.g., the product of the latter primitive roots...

Soldner. Its value is approximately μ ≈ 1.45136923488338105028396848589202744949303228… (sequence A070769 in the OEIS) Since the logarithmic integral is...

, s ) = e − ( x − μ ) / s s ( 1 + e − ( x − μ ) / s ) 2 = 1 s ( e ( x − μ ) / ( 2 s ) + e − ( x − μ ) / ( 2 s ) ) 2 = 1 4 s sech 2 ⁡ ( x − μ 2 s ) . {\displaystyle...

names, e.g., mu for μ, phi for φ. Every sequence is identified by the letter A followed by six digits, almost always referred to with leading zeros, e.g....

Given a random variable X ~ Norm[μ,σ] (a normal distribution with mean μ and standard deviation σ) and a constant L > μ, it can be shown via integration...

Constants". OEIS: A000796 OEIS: A019692 OEIS: A002193 OEIS: A002194 OEIS: A002163 OEIS: A001622 OEIS: A014176 OEIS: A002580 OEIS: A002581 OEIS: A010774 OEIS: A092526...

subset E of I, we also define the Gauss–Kuzmin measure of E μ ( E ) = 1 log ⁡ 2 ∫ E d x 1 + x . {\displaystyle \mu (E)={\frac {1}{\log 2}}\int _{E}{\frac...

factor will change as the Nusselt number changes. N u D = 0.027 R e D 4 / 5 P r 1 / 3 ( μ μ s ) 0.14 {\displaystyle \mathrm {Nu} _{D}=0.027\,\mathrm {Re}...

− 1 2 μ ^ ( u + τ , v ; τ ) = − μ ^ ( u , v ; τ ) e 2 8 π i μ ^ ( u , v ; τ + 1 ) = μ ^ ( u , v ; τ ) = − ( τ i ) − 1 2 e π i τ ( u − v ) 2 μ ^ ( u τ...

Greek alphabet to represent Greek numerals: they used a capital letter mu (Μ) to represent ten thousand.[citation needed] This Greek root was used in early...

μ − 3 ) x 4 + ( 3 − 2 μ ) x 3 − ( μ ) x 2 + ( 2 μ ) x − μ = 0 {\displaystyle x^{5}+(\mu -3)x^{4}+(3-2\mu )x^{3}-(\mu )x^{2}+(2\mu )x-\mu =0} where μ =...

representation Γ − 1 ( x ) = a + b x + ∫ − ∞ Γ ( α ) ( 1 x − t − t t 2 − 1 ) d μ ( t ) , {\displaystyle \Gamma ^{-1}(x)=a+bx+\int _{-\infty }^{\Gamma (\alpha...

\epsilon } By the previous lemma, we have μ ( T − n B 0 ∩ Δ n ) ≥ 1 2 μ ( B 0 ) μ ( Δ n ) ∈ 1 2 ( μ ( B ) ± ϵ ) μ ( Δ n ) {\displaystyle \mu (T^{-n}B_{0}\cap...

squarefree words. The Thue–Morse morphism μ is defined on alphabet {0,1} by the substitution map μ(0) = 01, μ(1) = 10: every 0 in a sequence is replaced...

reciprocals, two Euler products for the Möbius function μ(n) are ∏ p ∈ P ( 1 − 1 p s ) = ∑ n = 1 ∞ μ ( n ) n s = 1 ζ ( s ) {\displaystyle \prod _{p\,\in \...

that Q ( x ) = ∑ d ≤ x μ ( d ) ⌊ x d 2 ⌋ = ∑ d ≤ x x μ ( d ) d 2 + O ( ∑ d ≤ x 1 ) = x ∑ d ≤ x μ ( d ) d 2 + O ( x ) = x ∑ d μ ( d ) d 2 + O ( x ∑ d >...