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.

1680 equations across 1484 symbols.

P(at least one success in k tries)=1−(1−p)kP(\text{at least one success in } k \text{ tries}) = 1 - (1-p)^k

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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Q(st,at)←Q(st,at)+α[rt+1+γmax⁡aQ(st+1,a)−Q(st,at)]Q(s_t,a_t) \leftarrow Q(s_t,a_t) + \alpha\Big[r_{t+1} + \gamma \max_{a} Q(s_{t+1},a) - Q(s_t,a_t)\Big]

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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r=100,00092≈1,087 GPUs installed per day.r = \frac{100{,}000}{92} \approx 1{,}087 \text{ GPUs installed per day.}

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=fsh⋅nq⋅log⁡2K bits per second.R = \frac{f_s}{h} \cdot n_q \cdot \log_2 K \text{ bits per second.}

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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R(t)=1 ⁣[A(t)≥a∗]⋅1 ⁣[S(t)≥s∗]R(t) = \mathbb{1}\!\left[A(t) \ge a^{*}\right] \cdot \mathbb{1}\!\left[S(t) \ge s^{*}\right]

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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