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youtube-dl is a free and open source software tool for downloading video and audio from YouTube [2] and over 1,000 other video hosting websites. [3] It is released under the Unlicense software license. [4] As of September 2021, youtube-dl is one of the most starred projects on GitHub, with over 100,000 stars. [5]
In elementary algebra, the binomial theorem (or binomial expansion) describes the algebraic expansion of powers of a binomial.According to the theorem, it is possible to expand the polynomial (x + y) n into a sum involving terms of the form ax b y c, where the exponents b and c are nonnegative integers with b + c = n, and the coefficient a of each term is a specific positive integer depending ...
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Polynomial expansion. In mathematics, an expansion of a product of sums expresses it as a sum of products by using the fact that multiplication distributes over addition. Expansion of a polynomial expression can be obtained by repeatedly replacing subexpressions that multiply two other subexpressions, at least one of which is an addition, by ...
Pocket-sized creatures: Video shows teeny-tiny endangered crocodiles hatch. The Fort Worth Zoo welcomed two gharial crocodile hatchlings, a critically endangered reptile. The zoo, located in Texas ...
Repeated application of the recurrence relation for the lower incomplete gamma function leads to the power series expansion: [2] (,) = = (+) (+) = = (+ +). Given the rapid growth in absolute value of Γ(z + k) when k → ∞, and the fact that the reciprocal of Γ(z) is an entire function, the coefficients in the rightmost sum are well-defined, and locally the sum converges uniformly for all ...
August 5, 2024 at 11:58 AM. The artistic swimming competition begins today at the Paris 2024 Olympics, with one major change compared with previous games: Men are allowed to compete for the first ...
Binomial series. In mathematics, the binomial series is a generalization of the polynomial that comes from a binomial formula expression like for a nonnegative integer . Specifically, the binomial series is the MacLaurin series for the function , where and . Explicitly,