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searching for Empty sum 13 found (37 total)

alternate case: empty sum

Integer partition (3,388 words) [view diff] exact match in snippet view article find links to article

3 + 1 2 + 2 2 + 1 + 1 1 + 1 + 1 + 1 The only partition of zero is the empty sum, having no parts. The order-dependent composition 1 + 3 is the same partition

List of integer sequences (27 words) [view diff] exact match in snippet view article find links to article

C(n + 1, 2) = n(n + 1)/2 = 1 + 2 + ... + n for n ≥ 1, with t(0) = 0 (empty sum). A000217 Square numbers n2 0, 1, 4, 9, 16, 25, 36, 49, 64, 81, ... n2

Birth–death process (3,948 words) [view diff] exact match in snippet view article find links to article

_{j=1}^{k}\ln _{(j)}(n)}}+{\frac {c}{n\prod _{j=1}^{K}\ln _{(j)}(n)}},} where the empty sum for K = 1 {\displaystyle K=1} is assumed to be 0. The birth-and-death

Half-integer (803 words) [view diff] exact match in snippet view article find links to article

{\displaystyle n} is odd. This includes n = 0 {\displaystyle n=0} since the empty sum 0 is not half-integer. The negative of a half-integer is a half-integer

Root test (1,896 words) [view diff] exact match in snippet view article find links to article

_{(k)}(n)}}+{\frac {\rho _{n}}{n\prod _{k=1}^{K}\ln _{(k)}(n)}}.} (The empty sum is assumed to be 0.) The series converges, if lim inf n → ∞ ρ n > 1 {\displaystyle

Generating set of a group (1,746 words) [view diff] no match in snippet view article find links to article

\mathbb {N} _{>0}} . However, the integer 0 can not be expressed as a (non-empty) sum of 1s, thus {1} is not a semigroup generator of the natural numbers. Similarly

Local ring (2,299 words) [view diff] exact match in snippet view article find links to article

then it has a term that is a unit (this says in particular that the empty sum cannot be a unit, so it implies 1 ≠ 0). If these properties hold, then

Fenwick tree (2,289 words) [view diff] exact match in snippet view article find links to article

distinct powers of 2 (with k = 0 {\displaystyle k=0} representing an empty sum 0). For example, level k = 1 {\displaystyle k=1} contains nodes 1 = 2

Likelihood function (8,542 words) [view diff] exact match in snippet view article find links to article

log-likelihood, given no event, is 0, which corresponds to the value of the empty sum: without any data, there is no support for any models. The graph of the

König's theorem (set theory) (1,156 words) [view diff] exact match in snippet view article

and the index set I is finite. If I is empty, then the left sum is the empty sum and therefore 0, while the right product is the empty product and therefore

Ratio test (5,508 words) [view diff] exact match in snippet view article find links to article

_{(k)}(n)}}+{\frac {\rho _{n}}{n\prod _{k=1}^{K}\ln _{(k)}(n)}},\quad K\geq 1.} (The empty sum is assumed to be 0. With K = 1 {\displaystyle K=1} , the test reduces

Small-bias sample space (2,439 words) [view diff] exact match in snippet view article find links to article

equals 1 {\displaystyle 1} . For I = ∅ {\displaystyle I=\emptyset } , the empty sum is defined to be zero, and hence bias ∅ ( X ) = 1 {\displaystyle

Irrigation game (880 words) [view diff] exact match in snippet view article find links to article

\{root\}} be the player set, and for any coalition S {\displaystyle S} (the empty sum is 0) let v ( G ; c ) ( S ) = ∑ e ∈ A s c ( e ) . {\displaystyle v_{(G;c)}(S)=\sum