Live mathematical reference

Mathematical compendium

A live index of the equations in published articles. Each entry leads to its article, equation guide, and the terms explained there. New or edited published articles appear automatically.

1815 equations across 1477 symbols.

log⁡4(49)=log⁡2(7)≈2.8074log⁡4(48)≈2.7925\log_4(49) = \log_2(7) \approx 2.8074 \qquad \log_4(48) \approx 2.7925

1 published occurrence

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This equation gives an approximation: it relates the quantities while allowing an approximation.

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LSMEFT=LSM+∑iciΛ2Oi(6)+O ⁣(1Λ4)\mathcal{L}_{\text{SMEFT}} = \mathcal{L}_{\text{SM}} + \sum_i \frac{c_i}{\Lambda^{2}} \mathcal{O}_i^{(6)} + \mathcal{O}\!\left(\frac{1}{\Lambda^{4}}\right)

2 published occurrences

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This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.

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fl(xopy)=(xopy)(1+δ),∣δ∣≤u\mathrm{fl}(x \mathbin{\text{op}} y) = (x \mathbin{\text{op}} y)(1 + \delta), \qquad |\delta| \le u

1 published occurrence

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This equation states a bound: one expression must stay on the indicated side of the other under the article’s assumptions.

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price per token≳Cfixed+CenergyU⋅Tmax⁡+m\text{price per token} \gtrsim \frac{C_{\text{fixed}} + C_{\text{energy}}}{U \cdot T_{\max}} + m

1 published occurrence

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This mathematical expression combines the displayed quantities; its precise role follows from the surrounding article text.

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uc2(y)=∑i=1N(∂f∂xi)2u2(xi)  +  2∑i=1N−1∑j=i+1N∂f∂xi∂f∂xj u(xi,xj)u_c^2(y) = \sum_{i=1}^{N} \left(\frac{\partial f}{\partial x_i}\right)^2 u^2(x_i) \;+\; 2\sum_{i=1}^{N-1}\sum_{j=i+1}^{N} \frac{\partial f}{\partial x_i}\frac{\partial f}{\partial x_j}\, u(x_i, x_j)

1 published occurrence

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This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.

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Precision=TPR⋅pTPR⋅p+FPR⋅(1−p)\text{Precision} = \frac{\text{TPR} \cdot p}{\text{TPR} \cdot p + \text{FPR} \cdot (1-p)}

1 published occurrence

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This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.

All uses →Latest guide →Latest article →