E = mc²
iℏ ∂ψ/∂t = Ĥψ
e^(iπ) + 1 = 0
∫₋∞^∞ e^(-x²) dx = √π
ds² = c²dt² - dx² - dy² - dz²
Rμν - ½gμνR = 8πGTμν
S = k ln Ω
∇·E = ρ/ε₀
∇×B = μ₀J + μ₀ε₀ ∂E/∂t
ζ(s) = ∑(n=1)^∞ 1/n^s
χ(M) = V - E + F
K = det(∇²f) / (1 + |∇f|²)²
∂f/∂x
∫dx
∑n=1
lim→∞
∇²φ = 0
det(A)
sin²θ + cos²θ = 1
tan(α)
log(x)
e^x
π²/6
Γ(n) = (n-1)!
∂²u/∂t² = c²∇²u
curl F = ∇×F
div F = ∇·F
∮dr
P(A∩B) = P(A)·P(B|A)
E[X] = ∫₋∞^∞ x·f(x)dx
Var(X) = E[X²] - (E[X])²
∏p (1-p^(-s))^(-1)
∑k C(n,k) = 2^n
∫∫∫dV
α²+β²
x→0
n!
∞
≈
≠
≤
≥
±
∓
√
∛
∜
∂
∇
∫
∑
∏
f'(x) = lim(h→0) [f(x+h) - f(x)]/h
∫ udv = uv - ∫ vdu
(f∘g)'(x) = f'(g(x))·g'(x)
F(x) = ∫₋∞^x f(t) dt
d/dx ∫ₐ^x f(t) dt = f(x)
∫ₐ^b f'(x) dx = f(b) - f(a)
cos(α - β) = cos α cos β + sin α sin β
sin(α + β) = sin α cos β + cos α sin β
ln(1+x) = ∑(n=1)^∞ (-1)^(n+1) x^n/n
∫₀^∞ x^n e^(-x) dx = n!
B(p,q) = ∫₀^1 t^(p-1)(1-t)^(q-1) dt
ℱ[f(t)] = ∫₋∞^∞ f(t)e^(-2πift) dt
δ(x) = lim(ε→0) 1/(ε√π) e^(-x²/ε²)
∇f = (∂f/∂x, ∂f/∂y, ∂f/∂z)
∫∫∫ f(x,y,z) dV = ∫∫∫ f(r,θ,φ) r²sinφ dr dθ dφ
|A| = √(∑aᵢ²)
∂/∂x(∂u/∂y) = ∂/∂y(∂u/∂x)
∬ f(x,y) dA = ∫∫ f(r cosθ, r sinθ) r dr dθ
tan(α±β) = (tanα ± tanβ)/(1 ∓ tanα·tanβ)
log_a(xy) = log_a(x) + log_a(y)
⟨x|p⟩ = (2πℏ)^(-1/2) e^(ipx/ℏ)
∫₀^(π/2) sin^n x dx = (n-1)!!/n!! · π/2
Ψ(x,t) = ∑cₙφₙ(x)e^(-iEₙt/ℏ)
E = mc²
iℏ ∂ψ/∂t = Ĥψ
e^(iπ) + 1 = 0
∫₋∞^∞ e^(-x²) dx = √π
ds² = c²dt² - dx² - dy² - dz²
Rμν - ½gμνR = 8πGTμν
S = k ln Ω
∇·E = ρ/ε₀
∇×B = μ₀J + μ₀ε₀ ∂E/∂t
ζ(s) = ∑(n=1)^∞ 1/n^s
χ(M) = V - E + F
K = det(∇²f) / (1 + |∇f|²)²
∂f/∂x
∫dx
∑n=1
lim→∞
∇²φ = 0
det(A)
sin²θ + cos²θ = 1
tan(α)
log(x)
e^x
π²/6
Γ(n) = (n-1)!
∂²u/∂t² = c²∇²u
curl F = ∇×F
div F = ∇·F
∮dr
P(A∩B) = P(A)·P(B|A)
E[X] = ∫₋∞^∞ x·f(x)dx
Var(X) = E[X²] - (E[X])²
∏p (1-p^(-s))^(-1)
∑k C(n,k) = 2^n
∫∫∫dV
α²+β²
x→0
n!
∞
≈
≠
≤
≥
±
∓
√
∛
∜
∂
∇
∫
∑
∏
f'(x) = lim(h→0) [f(x+h) - f(x)]/h
∫ udv = uv - ∫ vdu
(f∘g)'(x) = f'(g(x))·g'(x)
F(x) = ∫₋∞^x f(t) dt
d/dx ∫ₐ^x f(t) dt = f(x)
∫ₐ^b f'(x) dx = f(b) - f(a)
cos(α - β) = cos α cos β + sin α sin β
sin(α + β) = sin α cos β + cos α sin β
ln(1+x) = ∑(n=1)^∞ (-1)^(n+1) x^n/n
∫₀^∞ x^n e^(-x) dx = n!
B(p,q) = ∫₀^1 t^(p-1)(1-t)^(q-1) dt
ℱ[f(t)] = ∫₋∞^∞ f(t)e^(-2πift) dt
δ(x) = lim(ε→0) 1/(ε√π) e^(-x²/ε²)
∇f = (∂f/∂x, ∂f/∂y, ∂f/∂z)
∫∫∫ f(x,y,z) dV = ∫∫∫ f(r,θ,φ) r²sinφ dr dθ dφ
|A| = √(∑aᵢ²)
∂/∂x(∂u/∂y) = ∂/∂y(∂u/∂x)
∬ f(x,y) dA = ∫∫ f(r cosθ, r sinθ) r dr dθ
tan(α±β) = (tanα ± tanβ)/(1 ∓ tanα·tanβ)
log_a(xy) = log_a(x) + log_a(y)
⟨x|p⟩ = (2πℏ)^(-1/2) e^(ipx/ℏ)
∫₀^(π/2) sin^n x dx = (n-1)!!/n!! · π/2
Ψ(x,t) = ∑cₙφₙ(x)e^(-iEₙt/ℏ)
E = mc²
iℏ ∂ψ/∂t = Ĥψ
e^(iπ) + 1 = 0
∫₋∞^∞ e^(-x²) dx = √π
ds² = c²dt² - dx² - dy² - dz²
Rμν - ½gμνR = 8πGTμν
S = k ln Ω
∇·E = ρ/ε₀
∇×B = μ₀J + μ₀ε₀ ∂E/∂t
ζ(s) = ∑(n=1)^∞ 1/n^s
χ(M) = V - E + F
K = det(∇²f) / (1 + |∇f|²)²
∂f/∂x
∫dx
∑n=1
lim→∞
∇²φ = 0
det(A)
sin²θ + cos²θ = 1
tan(α)
log(x)
e^x
π²/6
Γ(n) = (n-1)!
∂²u/∂t² = c²∇²u
curl F = ∇×F
div F = ∇·F
∮dr
P(A∩B) = P(A)·P(B|A)
E[X] = ∫₋∞^∞ x·f(x)dx
Var(X) = E[X²] - (E[X])²
∏p (1-p^(-s))^(-1)
∑k C(n,k) = 2^n
∫∫∫dV
α²+β²
x→0
n!
∞
≈
≠
≤
≥
±
∓
√
∛
∜
∂
∇
∫
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