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Longer titles found: Gaussian binomial coefficient (view), Central binomial coefficient (view)

searching for Binomial coefficient 27 found (263 total)

35 (number) (497 words) [view diff] exact match in snippet view article

Sequences. OEIS Foundation. Retrieved 2016-05-31. "Sloane's A000332 : Binomial coefficient binomial(n,4) = n*(n-1)*(n-2)*(n-3)/24". The On-Line Encyclopedia

Q-Vandermonde identity (859 words) [view diff] exact match in snippet view article find links to article

applications to quantum groups, a different q-binomial coefficient is used. This q-binomial coefficient, which we denote here by B q ( n , k ) {\displaystyle

Entropy (information theory) (10,074 words) [view diff] no match in snippet view article

In information theory, the entropy of a random variable quantifies the average level of uncertainty or information associated with the variable's potential

Bijective proof (400 words) [view diff] exact match in snippet view article find links to article

cream cones. Problems that admit bijective proofs are not limited to binomial coefficient identities. As the complexity of the problem increases, a bijective

P-adic analysis (1,043 words) [view diff] exact match in snippet view article find links to article

{x \choose k}={\frac {x(x-1)(x-2)\cdots (x-k+1)}{k!}}} is the kth binomial coefficient polynomial. Over the field of real numbers, the assumption that the

Gosper's algorithm (582 words) [view diff] exact match in snippet view article find links to article

from the original on 2019-04-12. Retrieved 2020-01-10. algorithm / binomial coefficient identities / closed form / symbolic computation / linear recurrences

1001 (number) (779 words) [view diff] exact match in snippet view article

in The Book of One Thousand and One Nights. "Sloane's A000332 : Binomial coefficient binomial(n,4) = n*(n-1)*(n-2)*(n-3)/24". The On-Line Encyclopedia

Theta divisor (492 words) [view diff] exact match in snippet view article find links to article

if h0(O(D)) = r + 1, the multiplicity of Wk at class(D) is the binomial coefficient ( g − k + r r ) . {\displaystyle {g-k+r \choose r}.} When k = g −

Sierpiński triangle (2,806 words) [view diff] exact match in snippet view article find links to article

Sierpiński triangle obtained by shading the first 25 (32) levels of a Pascal's triangle white if the binomial coefficient is even and black otherwise

John Selfridge (1,579 words) [view diff] exact match in snippet view article find links to article

Selfridge, J. L. (1993). "Estimates of the least prime factor of a binomial coefficient". Mathematics of Computation. 61 (203): 215–224. Bibcode:1993MaCom

Q-derivative (1,786 words) [view diff] exact match in snippet view article find links to article

{\displaystyle {\binom {n}{k}}_{q}} is the q {\displaystyle q} -binomial coefficient. By changing the order of summation as r = n − k {\displaystyle r=n-k}

Latin letters used in mathematics, science, and engineering (4,234 words) [view diff] exact match in snippet view article find links to article

electrical theory with indices denoting the number of combinations, a binomial coefficient together with a degree symbol (°), the Celsius measurement of temperature

Tensor algebra (4,161 words) [view diff] exact match in snippet view article find links to article

{\displaystyle v_{i}\cdot v_{j}=(i,j)v_{i+j}} where (i,j) denotes the binomial coefficient for ( i + j i ) {\displaystyle {\tbinom {i+j}{i}}} . This bialgebra

Beam splitter (4,872 words) [view diff] exact match in snippet view article find links to article

{\displaystyle M=n+m-N} and the ( n j ) {\displaystyle {\tbinom {n}{j}}} is a binomial coefficient and it is to be understood that the coefficient is zero if j ∉ {

Coupon collector's problem (2,814 words) [view diff] exact match in snippet view article find links to article

− 1 {\displaystyle f(x)={n-nx \choose n}^{-1}} .) Rewriting the binomial coefficient via the gamma function and expanding as the exp {\displaystyle \exp

Cofree coalgebra (1,708 words) [view diff] exact match in snippet view article find links to article

{\displaystyle v_{i}\cdot v_{j}=(i,j)v_{i+j}} where (i,j) denotes the binomial coefficient ( i + j i ) {\displaystyle {\tbinom {i+j}{i}}} . This bialgebra is

List of inventions in the medieval Islamic world (9,320 words) [view diff] exact match in snippet view article find links to article

theorem: The first formulation of the binomial theorem and the table of binomial coefficient can be found in a work by Al-Karaji, quoted by Al-Samaw'al in his

Harmonic number (5,558 words) [view diff] case mismatch in snippet view article find links to article

359–378. doi:10.1016/s0196-8858(03)00016-2. Wenchang Chu (2004). "A Binomial Coefficient Identity Associated with Beukers' Conjecture on Apery Numbers" (PDF)

Indian mathematics (13,945 words) [view diff] case mismatch in snippet view article find links to article

1007/1-4020-2321-9_7, ISBN 978-1-4020-2320-0. Fowler, David (1996), "Binomial Coefficient Function", The American Mathematical Monthly, 103 (1): 1–17, doi:10

Timeline of scientific discoveries (10,571 words) [view diff] exact match in snippet view article find links to article

integer logarithm. 850: Mahāvīra derives the expression for the binomial coefficient in terms of factorials, ( n r ) = n ! r ! ( n − r ) ! {\displaystyle

List of unsolved problems in mathematics (20,871 words) [view diff] exact match in snippet view article find links to article

(1971). "Research Problems: How often does an integer occur as a binomial coefficient?". American Mathematical Monthly. 78 (4): 385–386. doi:10.2307/2316907

Caputo fractional derivative (2,321 words) [view diff] exact match in snippet view article find links to article

\left(a+1\right)}{\Gamma \left(b+1\right)\cdot \Gamma \left(a-b+1\right)}}} is the binomial coefficient. Caputo-type fractional derivative is closely related to the Riemann–Liouville

Lifting-the-exponent lemma (2,217 words) [view diff] exact match in snippet view article find links to article

cannot be directly applied when p = 2 {\displaystyle p=2} because the binomial coefficient ( p 2 ) = p ( p − 1 ) 2 {\displaystyle {\binom {p}{2}}={\frac {p(p-1)}{2}}}

Purged cross-validation (1,352 words) [view diff] exact match in snippet view article find links to article

Then: The number of unique train-test combinations is given by the binomial coefficient: ( N k ) {\displaystyle {\binom {N}{k}}} Each observation is used

Smoothstep (2,725 words) [view diff] exact match in snippet view article find links to article

1, N - n) * Math.pow(x, N + n + 1); return result; } // Returns binomial coefficient without explicit use of factorials, // which can't be used with negative

Nome (mathematics) (13,963 words) [view diff] exact match in snippet view article

Index n Central binomial coefficient square [ ( 2 n − 2 ) ! ] 2 [ ( n − 1 ) ! ] 4 {\displaystyle {\frac {[(2n-2)!]^{2}}{[(n-1)!]^{4}}}} Sequence number

Spaces of test functions and distributions (19,154 words) [view diff] exact match in snippet view article find links to article

α {\displaystyle \beta \geq \alpha } we define their multi-index binomial coefficient as: ( β α ) := ( β 1 α 1 ) ⋯ ( β n α n ) . {\displaystyle {\binom