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%ما هو (من)٪ 1 - تعريف

TAYLOR SERIES

Newton's binomial series; Newton binomial; Newton's binomial; Newton binomial theorem

Gaussian binomial coefficient

FAMILY OF POLYNOMIALS

Q-binomial coefficient; Q-binomial; Gaussian coefficient; Gaussian binomial; Q-binomial theorem; Gaussian polynomial; Gaussian polynomials; Gaussian binomial coefficients; Q-binomial coefficients

In mathematics, the Gaussian binomial coefficients (also called Gaussian coefficients, Gaussian polynomials, or q-binomial coefficients) are q-analogs of the binomial coefficients. The Gaussian binomial coefficient, written as \binom nk_q or \begin{bmatrix}n\\ k\end{bmatrix}_q, is a polynomial in q with integer coefficients, whose value when q is set to a prime power counts the number of subspaces of dimension k in a vector space of dimension n over a finite field with q elements.

https://en.wikipedia.org/wiki/Gaussian_binomial_coefficient

Snowball sampling

NONPROBABILITY SAMPLING TECHNIQUE

Snowball sample; Respondent-driven sampling; Snowball method; Snowballed sample

In sociology and statistics research, snowball sampling (or chain sampling, chain-referral sampling, referral sampling (accessed 8 May 2011).Snowball Sampling, Changing Minds.

https://en.wikipedia.org/wiki/Snowball_sampling

Nyquist Theorem

THEOREM

Nyquist theorem; Shannon sampling theorem; Nyquist sampling theorem; Nyquist's theorem; Shannon-Nyquist sampling theorem; Nyquist-Shannon Sampling Theorem; Nyqvist-Shannon sampling theorem; Sampling theorem; Nyquist Sampling Theorem; Nyquist-Shannon sampling theorem; Nyquist–Shannon theorem; Nyquist–Shannon Theorem; Nyquist Theorem; Shannon-Nyquist theorem; Nyquist sampling; Nyquist's law; Nyquist law; Coherent sampling; Nyqvist limit; Raabe condition; Nyquist-Shannon Theorem; Nyquist-Shannon theorem; Nyquist noise theorem; Shannon–Nyquist theorem; Kotelnikov-Shannon theorem; Kotelnikov–Shannon theorem; Nyquist-Shannon; Kotelnikov theorem; Nyquist's sampling theorem; Sampling Theorem; Nyquist Shannon theorem; Nyquist–Shannon–Kotelnikov sampling theorem; Whittaker–Shannon–Kotelnikov sampling theorem; Whittaker–Nyquist–Kotelnikov–Shannon sampling theorem; Nyquist-Shannon-Kotelnikov sampling theorem; Whittaker-Shannon-Kotelnikov sampling theorem; Whittaker-Nyquist-Kotelnikov-Shannon sampling theorem; Cardinal theorem of interpolation; WKS sampling theorem; Whittaker–Kotelnikow–Shannon sampling theorem; Whittaker-Kotelnikow-Shannon sampling theorem; Nyquist–Shannon–Kotelnikov; Whittaker–Shannon–Kotelnikov; Whittaker–Nyquist–Kotelnikov–Shannon; Nyquist-Shannon-Kotelnikov; Whittaker-Shannon-Kotelnikov; Whittaker-Nyquist-Kotelnikov-Shannon; Whittaker–Shannon sampling theorem; Whittaker–Nyquist–Shannon sampling theorem; Whittaker-Nyquist-Shannon sampling theorem; Whittaker-Shannon sampling theorem

<communications> A theorem stating that when an analogue waveform is digitised, only the frequencies in the waveform below half the sampling frequency will be recorded. In order to reconstruct (interpolate) a signal from a sequence of samples, sufficient samples must be recorded to capture the peaks and troughs of the original waveform. If a waveform is sampled at less than twice its frequency the reconstructed waveform will effectively contribute only noise. This phenomenon is called "aliasing" (the high frequencies are "under an alias"). This is why the best digital audio is sampled at 44,000 Hz - twice the average upper limit of human hearing. The Nyquist Theorem is not specific to digitised signals (represented by discrete amplitude levels) but applies to any sampled signal (represented by discrete time values), not just sound. {Nyquist (http://geocities.com/bioelectrochemistry/nyquist.htm)} (the man, somewhat inaccurate). (2003-10-21)

ويكيبيديا

Binomial series

In mathematics, the binomial series is a generalization of the polynomial that comes from a binomial formula expression like $(1+x)^{n}$ for a nonnegative integer $n$ . Specifically, the binomial series is the Taylor series for the function $f(x)=(1+x)^{\alpha }$ centered at $x=0$ , where $\alpha \in \mathbb {C}$ and $|x|<1$ . Explicitly,

where the power series on the right-hand side of (1) is expressed in terms of the (generalized) binomial coefficients

{\binom {\alpha }{k}}:={\frac {\alpha (\alpha -1)(\alpha -2)\cdots (\alpha -k+1)}{k!}}.

https://en.wikipedia.org/wiki/Binomial series