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...ly unique 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 == ...

{{Short description|Special cases of the Fourier series}} {{distinguish-redirect|Sine and cosine series|Sine and cosine#Series definitions}} ...

{{Distinguish|Bourne (film series)}} ...operator <math> G_0 V </math>. In general the first few terms of the Born series are good approximation to the expanded quantity for "weak" interaction <mat ...

...'''rational series''' is a generalisation of the concept of [[formal power series]] over a [[ring (mathematics)|ring]] to the case when the basic algebraic s A ''formal series'' is a ''R''-valued function ''c'', on the [[free monoid]] ''A''<sup>*</sup ...

* {{cite book | first=Alan | last=Baker | authorlink=Alan Baker (mathematician) | title=T ...ink2=Gisbert Wüstholz | title=Logarithmic Forms and Diophantine Geometry | series=New Mathematical Monographs | volume=9 | publisher=[[Cambridge University P ...

...o terms are of orders that have a certain "gap" between them. Such a power series is "badly behaved" in the sense that it cannot be extended to be an [[analy ...b>''j''∈'''N'''</sub> be a sequence of complex numbers such that the power series ...

...iables produced by multiple individuals (the first dimension), in multiple series (the second dimension) at multiple times periods (the third dimension) and where ''i'' is the individual dimension, ''s'' is the series dimension, ''t'' is the time dimension, and ''h'' is the horizon dimension. ...

...having a second derivative at a point means having a second-order [[Taylor series|Taylor expansion]] at that point with a local error smaller than any quadra * {{cite book | title=Convex Functions and their Applications: A Contemporary Approach | ...

The [[power series]] ...ermined by its characteristic power series ''Q''(''z''), and every [[power series]] with constant term 1 gives rise to a multiplicative sequence. ...

{{Short description|Summability method for a class of divergent series}} ...' is a summability method for summing infinite series related to [[Lambert series]] specially relevant in analytic number theory. ...

[[File:Fourier transform, Fourier series, DTFT, DFT.svg|thumb|400px|A Fourier transform and 3 variations caused by p ...ntity is a form of the [[Poisson summation formula]]. Similarly, a Fourier series whose coefficients are samples of <math>s(t)</math> at constant intervals ( ...

...t3=Pogány | first3=Tibor K. | title=Lecture Notes in Mathematics | chapter=Series of Bessel and Kummer-Type Functions | publisher=Springer International Publ ...epler's equation]] <math>M=E-e\sin E</math> can be expressed via a Kapteyn series:<ref name="Baricz_etal" /><ref name="Borghi p. ">{{cite arXiv | last=Borghi ...

...absolutely convergent Fourier series has an absolutely convergent Fourier series under some conditions. The theorem was named after [[Norbert Wiener]] and [ ...hen its inverse {{math|1/''f''}} also has an absolutely convergent Fourier series. ...

...shida | first=Makoto | title=The genus fields of algebraic number fields | series=Lecture Notes in Mathematics | volume=555 | publisher=[[Springer-Verlag]] | ...umber Fields | year=1973 | publisher=Academic Press | isbn=0-12-380250-4 | series=Pure and Applied Mathematics | volume=55 | zbl=0307.12001 }} ...

...used to [[series acceleration|accelerate the convergence]] of an infinite series. The method was first suggested by [[Ernst Kummer]] in 1837. ...th>a_n-\gamma \,b_n</math> is always also a sequence going to zero and the series given by the difference, <math>\sum_{n=1}^\infty (a_n-\gamma\, b_n)</math>, ...

...éric|last2=Déglise|title=Triangulated Categories of Mixed Motives|chapter=|series=Springer Monographs in Mathematics|year=2019|doi=10.1007/978-3-030-33242-6| ...drei|publisher=[[Princeton University Press]]|year=2000|isbn=9780691048147|series=Annals of Mathematics Studies, vol. 143|location=|pages=10&ndash;86|chapter ...

...ants of ''n''×''n'' matrices | zbl=0714.16001 | series=Regional Conference Series in Mathematics | volume=78 | location=Providence, RI | publisher=[[American ...

...ely | first2=Tamás | title=Central simple algebras and Galois cohomology | series=Cambridge Studies in Advanced Mathematics | volume=101 | location=Cambridge * {{cite book | page=[https://archive.org/details/handbookofalgebr0003unse/page/282 282] ...

...cription|In mathematics, series built from equally spaced terms of another series}} ...cted unaltered from the original series. Formally, if one is given a power series ...

...ref>{{cite journal|jstor=24900534|author=Rudin, Walter|title=Trigonometric series with gaps|journal=Journal of Mathematics and Mechanics|year=1960|volume=9 | ...