...nce sets, the families using higher-order residues and also the twin prime power series, see [[#References|[a1]]], Sect. VI.8. The families of difference se
...exist whenever $q$ is a power of $2$ or $3$ or the square of an odd prime power; see [[#References|[a1]]], Sect. VI.9–12, for the construction of all the
9 KB (1,331 words) - 19:36, 13 February 2024
...functions in combinatorics considerable use is made of algebras of formal power series and of various symbolic methods (cf. [[#References|[1]]], [[#Referen
...that take real values and are such that $f(x,y) = 0$ unless $x \le y$. The sum of two such functions and multiplication by a number are defined in the usu
8 KB (1,343 words) - 08:52, 12 November 2023
of formal power series in $ n $
formal power series in $ 2n $
17 KB (2,537 words) - 22:38, 15 December 2019
In mathematical analysis, the need arises to generalize the concept of the sum of a series (limit of a sequence, value of an integral) to include the case
If the sum of the series is defined as
10 KB (1,530 words) - 08:24, 6 June 2020
The field concerned with best rational approximation to power series. Let
f( z) = \sum _ {k=0}^ \infty f _ {k} z ^ {k}
15 KB (2,227 words) - 13:32, 11 November 2023
...[[#References|[a46]]], and all papers by Turán mentioned below) the power sum method, by which one can investigate certain minimax problems described bel
Bohr norm: $M _ { 0 } ( k ) = \sum _ { j = 1 } ^ { n } | b _ { j } \| z _ { j } | ^ { k }$;
40 KB (5,729 words) - 17:51, 5 May 2024
w _ {k} ( \xi \oplus \eta ) = \sum _ { i } w _ {i} ( \xi ) w _ {k- i} ( \eta ),\ \
are rings of formal power series in the Stiefel–Whitney classes:
5 KB (692 words) - 17:18, 6 January 2024
...}$ in place of ${\cal R }_ { q ^ { 2 } }$ above (and now take an infinite sum in the exponential). It does not, however, live in the algebraic tensor pro
\begin{equation*} \phi h = \sum h _{( 2 )} \phi_{ ( 2 )} \langle S h _ { ( 1 ) } , \phi _ { ( 1 ) } \rangle
14 KB (2,048 words) - 18:24, 3 August 2020
\sum _ { k= 0} ^ \infty u _ {k} ( z),
then the sum $ s ( z) $
22 KB (3,120 words) - 01:51, 24 February 2022
then the series \eqref{2} is absolutely summable by the method $A$ to the sum $s$. Condition \eqref{1} is an additional requirement which makes absolute
...ries. If each such series is summable by this method to a sum equal to the sum to which it converges, then the method is called absolutely regular. For in
5 KB (850 words) - 15:41, 14 February 2020
of a power series
f _ \infty = f _ \infty ( z) = \sum _{k=0} ^ \infty c _ {k} z ^ {-k}
13 KB (1,972 words) - 20:02, 15 January 2024
...butive lattice]] (see also [[FKG inequality|FKG inequality]]), such as the power set of a finite set ordered by proper inclusion. For subsets $ A $,
let $ f ( A ) = \sum _ {a \in A } f ( a ) $.
4 KB (523 words) - 19:25, 4 April 2020
\begin{equation*} D_ { n } ( x , a ) = \sum _ { i = 0 } ^ { \lfloor n / 2 \rfloor } \frac { n } { n - i } \left( \begin
\begin{equation*} \sum _ { n = 0 } ^ { \infty } D _ { n } ( x , a ) z ^ { n } = \frac { 2 - x z }
15 KB (2,207 words) - 16:45, 1 July 2020
...functions, up to an arbitrary order, are summable to a given degree with a power weight. For such cases the imbeddings of weighted spaces have been studied
\sum _ {| k | = l } | ( 1 + | x |) ^ {- \alpha } D ^ {k} f ;
9 KB (1,435 words) - 08:13, 13 January 2024
\begin{equation*} s _ { \lambda } = \sum _ { T } \mathbf{x} ^ { T }, \end{equation*}
where the sum is over all semi-standard Young tableaux of shape $\lambda$ with entries be
14 KB (2,001 words) - 10:09, 11 November 2023
The sum of the powers of any term of a polynomial is called the ''degree'' of that
...ower of $x_1$ is higher, and if these powers are equal, that for which the power of $x_2$ is higher, etc. If all terms of a polynomial are ordered so that e
9 KB (1,497 words) - 10:44, 27 June 2015
a Riemann sum, $ \sum _ \varpsi f = \sum _ {i = 1 } ^ {n} f ( x _ {i} ) ( a _ {i} - a _ {i - 1 } ) $.
\left | {\sum _ \varpsi f - I } \right | < \epsilon.
11 KB (1,718 words) - 22:15, 5 June 2020
where the sum is over all strings $i_1,\ldots,i_k$, $i_j \ge 1$, such that $i_1+\cdots+i_
where the sum is over all $r \in \mathbf{N}$ and pairs of order-preserving injective mapp
4 KB (709 words) - 13:46, 20 March 2023
...negative. A line bundle is said to be big if the sections of some positive power of $L$ give a [[Birational mapping|birational mapping]] of $X$ into project
...line bundle $E$ plus an effective divisor (cf. [[Divisor|Divisor]]) $D = \sum _ { k = 1 } ^ { r } a _ { k } D _ { k }$, where $a_k$ are positive integers
8 KB (1,253 words) - 15:30, 1 July 2020
is endowed with the natural structure of a Hopf algebra. Let $ A = \sum _ {n \in \mathbf Z} A _{n} $
modules. Then $ A ^{*} = \sum _ {n \in \mathbf Z} A _{n} ^{*} $ ,
11 KB (1,576 words) - 08:51, 16 December 2019