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Polyphase sequences are an important class of sequences and play important roles in synchronizing sequence design. [[Category:Sequences and series]] ...

{{Short description|Mathematical concept concerning infinite sequences}} ...is]], the space '''bs''' consists of all infinite [[Sequence (mathematics)|sequences]] (''x''_''i'') of [[real numbers]] <math>\R</math> or [[complex ...

...ue or well-defined, but the general idea is to find a formula for a series and then evaluate it outside its [[radius of convergence]]. == Common divergent series == ...

...m also is a multiple of the other term. The concept can be generalized to sequences with values in any [[ring (mathematics)|ring]] where the concept of [[divis ...ore, by the strong divisibility property, <math>\gcd(a_m,a_n) = a_m</math> and therefore <math>a_m\mid a_n</math>. ...

{{Short description|Mathematical series, portmanteau of "Fibonacci" and "factorial"}} ...F''_''i''}} is the {{math|''i''}}^th Fibonacci number, and {{math|0!_''F''}} gives the [[empty product]] (defined as the [[m ...

...[[integer sequence]] whose multiples include [[almost all]] integers. The sequences are named after [[Felix Behrend]]. If <math>A</math> is a sequence of integers greater than one, and if <math>M(A)</math> denotes the set of positive integer multiples of membe ...

...equence|''k''-automatic sequences]] and [[k-regular sequence|''k''-regular sequences]]. ...3975(93)90230-Q | doi-access = }}</ref> [[Rational set#Rational relations and rational functions|rational relation]] over Σ^&lowast;&nbsp;×&nbs ...

...every sequence ''x''_''n'' of positive integers, the sum of the series ...2004 |isbn=0-387-20860-7 | zbl=1058.11001 | contribution=E24 Irrationality sequences|page=346|url=https://books.google.com/books?id=1AP2CEGxTkgC&pg=PA346 }}.</r ...

{{short description|On when a morphism of spectral sequences in homological algebra is an isomorphism}} ...st quadrant spectral sequences of [[flat module]]s over a commutative ring and <math>f: E^r \to {}^{\prime}E^r</math> a morphism between them. Then any tw ...

...]s that is satisfied precisely if [[weak topology|weak convergence]] of '''sequences''' entails convergence in norm. ...converge to <math>x</math> in norm? A canonical example of this property, and commonly used to illustrate the Schur property, is the <math>\ell_1</math> ...

...t the terms of the sequence to be fractions, but surprisingly, a few Somos sequences have the property that all of their members are integers. ...e recursions are very simple (there is no addition on the right-hand side) and they define the all-ones sequence (1, 1, 1, 1, 1, 1, ...). In the first no ...

...ort of arithmetic convolution: the product of <math>(a_1, a_2, ...)</math> and <math>(b_1, b_2, ...)</math> has components ...th> is the [[least common multiple]] of <math>i</math> and <math>j</math>, and <math>(i,j)</math> is their [[greatest common divisor]]. ...

{{Short description|A pair of collections of integer sequences with no such sequence lying between them.}} ...orff gaps shows that the partially ordered set of possible growth rates of sequences is not complete. ...

...''n''^th digit of x_''k'' is '''4''' if ''n'' ≤ ''k'' and the ''n''th [[Turing machine]] in a computable [[Gödel numbering]] halts on ...bound principle]] of real analysis, even when considering only computable sequences. ...

...spectral sequence]] relating the homology with mod&nbsp;''p'' coefficients and the homology reduced mod&nbsp;''p''. It is named after [[Meyer Bockstein]] Let ''C'' be a chain complex of [[torsion-free abelian group]]s and ''p'' a [[prime number]]. Then we have the exact sequence: ...

...e Auslander|first2=Idun |last2=Reiten|author2-link=Idun Reiten|year=1975}} and developed by them in several subsequent papers. ...rvtxt|Auslander|1982}}, {{harvtxt|Gabriel|1980}}, {{harvtxt|Reiten|1982}}, and the book {{harvtxt|Auslander|Reiten|Smalø|1997}}. Many of the original pape ...

*The lower [[natural density]], the [[Limit superior and limit inferior|inferior limit]] as <math>n</math> goes to infinity of the p .../math> for which the upper natural density differs from the lower density, and for which the natural density itself does not exist.{{r|b}} ...

| series = Second Series ...> of the [[Hilbert space]] of square summable sequences, consisting of the sequences whose elements are all [[rational number]]s. ...

{{Short description|Sequence of numbers consisting of 1 and -1}} {{about|sign sequences in mathematics|sequences of roadside signs|Burma-Shave}} ...

{{Short description|Space of bounded sequences}} {{About|the vector spaces of sequences and functions|the finite-dimensional vector space distance|Chebyshev distance}} ...