...By the complexity of a diagram of functional elements one understands the sum of the weights of all functional elements that are present in this diagram.
...ts are equal to 1; or 2) the weight of a threshold element is equal to the sum of the absolute values of all coefficients $ w _ {i} $(
12 KB (1,820 words) - 11:43, 26 March 2023
} \cdot \sum _ {n \leq x } \left | {f ( n ) } \right | ^ {q} \right ) ^ { {1 / q } } .
} \cdot \sum _ {n \leq x } f ( n )
5 KB (715 words) - 10:00, 9 January 2021
The permutation is chosen so that the power of Wilcoxon's test for the given alternative is highest. The statistical di
cf. [[Rank sum test|Rank sum test]]; [[Mann–Whitney test|Mann–Whitney test]]). See also [[Van der Wa
3 KB (399 words) - 10:34, 7 February 2021
\sum _ {k = 0 } ^ { {n } - 1 } e _ {k} u _ {k} ,
\sum _ {k = 0 } ^ { {n } - 1 } w ^ {(} k) e _ {k} = 0,
5 KB (724 words) - 22:11, 5 June 2020
with all coordinates equal, but not a power of an element — a concept that is not defined in an arbitrary vector spac
\sum _ {\begin{array}{c}
2 KB (316 words) - 22:10, 5 June 2020
...problem|Goldbach problem]]); and the representation of a given number as a sum of one prime number and two squares (cf. [[Hardy–Littlewood problem|Hardy
...atic results in this field were obtained in 1748 by L. Euler, who employed power series to study the partition of integers into positive summands; in partic
10 KB (1,609 words) - 13:03, 8 February 2020
\begin{equation*} S = \sum _ { n \in A } e ^ { 2 \pi i f ( n ) }, \end{equation*}
...$f$ is a real-valued function (cf. also [[Trigonometric sum|Trigonometric sum]]). The basic problem is to show, under suitable circumstances, that $S = o
10 KB (1,528 words) - 07:11, 24 January 2024
\sum _ { i = 1 } ^ { k } \
\sum _ {\nu = 1 } ^ { {\alpha _ i } }
9 KB (1,382 words) - 08:27, 6 June 2020
...$ is summable by the Cesàro method of order $k$, or $(C,k)$-summable, with sum $S$ if
...eries is summable by the method $(C,k)$, then it is summable with the same sum by the method $(C,k')$ for $k' > k > -1$. This property does not hold for $
3 KB (519 words) - 15:44, 7 May 2012
$ \sum m _ {i} = | m | \geq 2 $
...case one says that one has [[Small denominators|small denominators]]), the power series $ x = y + \dots $
7 KB (1,085 words) - 08:13, 6 June 2020
\sum _ {r = 0 } ^ \infty
...on-central "chi-squared" distribution appears as the distribution of the sum of squares of independent random variables $ X _ {1} \dots X _ {n} $
4 KB (556 words) - 18:53, 24 January 2024
...bo looked for an algebra that is $8$-dimensional over the complex numbers, power-associative and, unlike the [[octonion]] algebra, has the [[Lie algebra|Lie
\begin{equation*} e _ { j } * e _ { k } = \sum _ { l = 1 } ^ { 8 } ( \sqrt { 3 } d _ { j k l } - f _ { j k l } ) e _ { l }
7 KB (944 words) - 10:21, 8 March 2021
...pediaofmath.org/legacyimages/b/b015/b015210/b01521051.png" />; the ordinal sum is defined uniquely up to an isomorphism, by specifying the components and
10 KB (1,447 words) - 17:26, 7 February 2011
and the Chern polynomial as an element of the formal power series ring $ H ^ {**} ( \mathop{\rm BU} _ {n} ) [ [ t ] ] $.
in other words $ c _ {k} ( \xi \oplus \eta ) = \sum _ {i} c _ {i} ( \xi ) c _ {k-i} ( \eta ) $
13 KB (1,910 words) - 19:40, 7 January 2024
''of a power series
\sum _ {k = 0 } ^ \infty
4 KB (602 words) - 19:35, 5 June 2020
\sum _ { n=0 } ^ \infty a _ {n} $$
is summable by Abel's method to a sum $ S $
11 KB (1,603 words) - 10:19, 7 May 2021
associated with a graded ring $ R = \sum _ {n=0} ^ \infty R _ {n} $(
does not contain $ \sum _ {n=1} ^ \infty R _ {n} $.
3 KB (468 words) - 09:09, 6 January 2024
denotes the algebra of all power series $ \sum a _ \alpha z _ {1} ^ {\alpha _ {1} } \dots z _ {n} ^ {\alpha _ {n} } $
$ | \alpha | = \sum \alpha _ {i} $).
8 KB (1,161 words) - 08:25, 6 June 2020
A power series which offers a complete solution to the problem of local inversion o
\sum _ {n = 1 } ^ \infty {
5 KB (731 words) - 06:29, 30 May 2020
represented by a power series
\sum _ {v = 0 } ^ \infty
5 KB (790 words) - 08:29, 20 January 2024