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

searching for Binomial coefficient 34 found (258 total)

Q-Vandermonde identity (858 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) (9,711 words) [view diff] no match in snippet view article

In information theory, the entropy of a random variable is the average level of "information", "surprise", or "uncertainty" inherent to the variable's

35 (number) (542 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

15 (number) (1,061 words) [view diff] exact match in snippet view article

Sequences. OEIS Foundation. Sloane, N. J. A. (ed.). "Sequence A000332 (Binomial coefficient binomial(n,4) = n*(n-1)*(n-2)*(n-3)/24)". The On-Line Encyclopedia

P-adic analysis (1,296 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

Bijective proof (706 words) [view diff] exact match in snippet view article find links to article

{n}{n-k}}} . Problems that admit bijective proofs are not limited to binomial coefficient identities. As the complexity of the problem increases, a bijective

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 (2,673 words) [view diff] exact match in snippet view article find links to article

Sierpinski 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 (1,575 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". Math. Comput. 61 (203): 215–224. Bibcode:1993MaCom..61..215E. doi:10

Möbius function (2,663 words) [view diff] exact match in snippet view article find links to article

\mu _{k}\left(p^{a}\right)=(-1)^{a}{\binom {k}{a}}\ } where the binomial coefficient is taken to be zero if a > k. The definition may be extended to complex

Q-derivative (1,782 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}

Artin–Hasse exponential (1,067 words) [view diff] exact match in snippet view article find links to article

expansion of (1 - xn)a are p-integral by p-adic continuity of the binomial coefficient polynomials t(t-1)...(t-k+1)/k! in t together with their obvious

1001 (number) (677 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

Latin letters used in mathematics, science, and engineering (3,835 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 (4,160 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

Binomial transform (2,375 words) [view diff] exact match in snippet view article find links to article

d ) ) {\displaystyle {\binom {\nu _{p}(n)}{\nu _{p}(d)}}} is the binomial coefficient. This convolution appears in the book by P. J. McCarthy (Introduction

Beam splitter (4,653 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 ∉ {

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

Stanley sequence (1,140 words) [view diff] exact match in snippet view article find links to article

n {\displaystyle n} such that the n {\displaystyle n} th central binomial coefficient is 1 mod 3, and the numbers whose balanced ternary representation

List of inventions in the medieval Islamic world (9,599 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

Indian mathematics (13,585 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

Harmonic number (5,518 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)

Timeline of scientific discoveries (10,204 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 (19,531 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

1000 (number) (25,229 words) [view diff] exact match in snippet view article

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

Lifting-the-exponent lemma (2,048 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}}}

Distribution (mathematics) (21,600 words) [view diff] exact match in snippet view 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

Super-resolution optical fluctuation imaging (2,242 words) [view diff] exact match in snippet view article find links to article

represents the moments. The term within the brackets indicates a binomial coefficient. This way of computation is straightforward in comparison with calculating

Pascal's pyramid (3,341 words) [view diff] exact match in snippet view article find links to article

examples in 3 and 2 dimensions, respectively. ^2 The formula for the binomial coefficient is usually expressed as n!/x!(n−x)!, where n−x = y. Arbitrary layer

Smoothstep (2,446 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) (13,956 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

Generating function transformation (11,127 words) [view diff] exact match in snippet view article find links to article

parameter x {\displaystyle x} . These relations also still hold if the binomial coefficient substitution of ( n k ) ⟼ ( n + p k + p ) {\displaystyle {\binom

Spaces of test functions and distributions (18,993 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