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.

1676 equations across 1477 symbols.

⟨σv⟩3α  ∝  ΓαΓ Γrad  exp⁡ ⁣(−ERkBT)\langle \sigma v \rangle_{3\alpha} \;\propto\; \frac{\Gamma_\alpha}{\Gamma}\,\Gamma_{\mathrm{rad}}\; \exp\!\left(-\frac{E_R}{k_{B}T}\right)

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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L(u)={1,u≤7×108g,u>7×108L(u) = \begin{cases} 1, & u \le 7 \times 10^{8} \\ g, & u > 7 \times 10^{8} \end{cases}

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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qA(v)≷qB(v),where the sign can flip as the operating-point vector v variesq_A(v) \gtrless q_B(v), \quad \text{where the sign can flip as the operating-point vector } v \text{ varies}

1 published occurrence

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

All uses →Latest guide →Latest article →