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Table of contents: Sums and products - Extreme values - Limits - Derivatives - Integrals - Indefinite integrals

Sums and products

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Symbol: Sum nf ⁣(n)\sum_{n} f\!\left(n\right) Sum
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Symbol: Product nf ⁣(n)\prod_{n} f\!\left(n\right) Product
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Symbol: PrimeSum pf ⁣(p)\sum_{p} f\!\left(p\right) Sum over primes
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Symbol: PrimeProduct pf ⁣(p)\prod_{p} f\!\left(p\right) Product over primes
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Symbol: DivisorSum knf ⁣(k)\sum_{k \mid n} f\!\left(k\right) Sum over divisors
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Symbol: DivisorProduct knf ⁣(k)\prod_{k \mid n} f\!\left(k\right) Product over divisors

Extreme values

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Symbol: Supremum supP(x)f ⁣(x)\mathop{\operatorname{sup}}\limits_{P\left(x\right)} f\!\left(x\right) Supremum of a set or function
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Symbol: Infimum infP(x)f ⁣(x)\mathop{\operatorname{inf}}\limits_{P\left(x\right)} f\!\left(x\right) Infimum of a set or function
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Symbol: Minimum minP(x)f ⁣(x)\mathop{\min}\limits_{P\left(x\right)} f\!\left(x\right) Minimum value of a set or function
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Symbol: Maximum maxP(x)f ⁣(x)\mathop{\max}\limits_{P\left(x\right)} f\!\left(x\right) Maximum value of a set or function
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Symbol: ArgMin arg minP(x)f ⁣(x)\mathop{\operatorname{arg\,min}}\limits_{P\left(x\right)} f\!\left(x\right) Locations of minimum value
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Symbol: ArgMax arg maxP(x)f ⁣(x)\mathop{\operatorname{arg\,max}}\limits_{P\left(x\right)} f\!\left(x\right) Locations of maximum value
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Symbol: ArgMinUnique arg min*P(x)f ⁣(x)\mathop{\operatorname{arg\,min*}}\limits_{P\left(x\right)} f\!\left(x\right) Unique location of minimum value
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Symbol: ArgMaxUnique arg max*P(x)f ⁣(x)\mathop{\operatorname{arg\,max*}}\limits_{P\left(x\right)} f\!\left(x\right) Unique location of maximum value

Limits

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Symbol: Limit limxaf ⁣(x)\lim_{x \to a} f\!\left(x\right) Limiting value
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Symbol: SequenceLimit limnaf ⁣(n)\lim_{n \to a} f\!\left(n\right) Limiting value of sequence
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Symbol: RealLimit limxaf ⁣(x)\lim_{x \to a} f\!\left(x\right) Limiting value, real variable
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Symbol: LeftLimit limxaf ⁣(x)\lim_{x \to {a}^{-}} f\!\left(x\right) Limiting value, from the left
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Symbol: RightLimit limxa+f ⁣(x)\lim_{x \to {a}^{+}} f\!\left(x\right) Limiting value, from the right
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Symbol: ComplexLimit limzaf ⁣(z)\lim_{z \to a} f\!\left(z\right) Limiting value, complex variable
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Symbol: MeromorphicLimit limzaf ⁣(z)\lim_{z \to a} f\!\left(z\right) Limiting value, allowing poles

Derivatives

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Symbol: Derivative ddzf ⁣(z)\frac{d}{d z}\, f\!\left(z\right) Derivative
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Symbol: RealDerivative ddxf ⁣(x)\frac{d}{d x}\, f\!\left(x\right) Real derivative
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Symbol: ComplexDerivative ddzf ⁣(z)\frac{d}{d z}\, f\!\left(z\right) Complex derivative
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Symbol: ComplexBranchDerivative ddzf ⁣(z)\frac{d}{d z}\, f\!\left(z\right) Complex derivative, allowing branch cuts
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Symbol: MeromorphicDerivative ddzf ⁣(z)\frac{d}{d z}\, f\!\left(z\right) Complex derivative, allowing poles

Integrals

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Symbol: Integral abf ⁣(x)dx\int_{a}^{b} f\!\left(x\right) \, dx Integral

Indefinite integrals

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Symbol: IndefiniteIntegralEqual f ⁣(x)dx=g ⁣(x)+C\int f\!\left(x\right) \, dx = g\!\left(x\right) + \mathcal{C} Indefinite integral
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Symbol: RealIndefiniteIntegralEqual f ⁣(x)dx=g ⁣(x)+C\int f\!\left(x\right) \, dx = g\!\left(x\right) + \mathcal{C} Indefinite integral, real derivative
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Symbol: ComplexIndefiniteIntegralEqual f ⁣(x)dx=g ⁣(x)+C\int f\!\left(x\right) \, dx = g\!\left(x\right) + \mathcal{C} Indefinite integral, complex derivative

Copyright (C) Fredrik Johansson and contributors. Fungrim is provided under the MIT license. The source code is on GitHub.

2019-07-15 23:42:41.550119 UTC