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.

g(RD)=11+3q2RD2/π2,q=ln⁡10400≈0.0057565g(\mathrm{RD}) = \frac{1}{\sqrt{1 + 3q^2 \mathrm{RD}^2 / \pi^2}}, \qquad q = \frac{\ln 10}{400} \approx 0.0057565

1 published occurrence

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

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r′=r+q1/RD2+1/d2∑j=1mg(RDj)(sj−E(s∣r,rj,RDj))r' = r + \frac{q}{1/\mathrm{RD}^2 + 1/d^2} \sum_{j=1}^{m} g(\mathrm{RD}_j)\left(s_j - E(s \mid r, r_j, \mathrm{RD}_j)\right)

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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Tfleet=N⋅Pdevice⋅Usustained⋅AT_{\mathrm{fleet}} = N \cdot P_{\mathrm{device}} \cdot U_{\mathrm{sustained}} \cdot A

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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Var(N)⟨N⟩2≥2kBΔStot\frac{\mathrm{Var}(N)}{\langle N \rangle^2} \geq \frac{2 k_B}{\Delta S_{\text{tot}}}

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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