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[[File:PM vs PN expansion EN.svg|thumb|Post-minkowskian vs Post-newtonian expansions|419x419px]] ...solutions of [[Einstein's equations]] by means of a [[Taylor series|power series development]] of the [[metric tensor]]. ...

...calculus]] that hold for finite expansions even when manipulating infinite expansions. An example<ref name=Koetsier/> is Euler's derivation of the series ...

...eihMuwkh4DsC | publisher=[[Springer-Verlag]] | location=Berlin, New York | series=Ergebnisse der Mathematik und ihrer Grenzgebiete. Neue Folge. | mr=0094466 ...

...eering problems related to transport of thermal<ref>Z. Altaç, Exact series expansions, recurrence relations, properties and integrals of the generalized exponent == Series expansions == ...

...eihMuwkh4DsC | publisher=[[Springer-Verlag]] | location=Berlin, New York | series=Ergebnisse der Mathematik und ihrer Grenzgebiete. Neue Folge. | mr=0094466 ...

{{Short description|Technique to find asymptotic expansions}} ...xtension of the [[steepest descent method]] for getting uniform asymptotic expansions in the case of coalescing [[saddle point]]s.<ref>{{cite book|first1=Frank W ...

|title = Polynomial expansions of analytic functions |series = Ergebnisse der Mathematik und ihrer Grenzgebiete. Neue Folge. ...

...eihMuwkh4DsC | publisher=[[Springer-Verlag]] | location=Berlin, New York | series=Ergebnisse der Mathematik und ihrer Grenzgebiete. Neue Folge. | mr=0094466 *{{Citation | last1=Narumi | first1=S. | title=On a power series having only a finite number of algebraico logarithmic singularities on its ...

...rlin, New York | journal=Ergebnisse der Mathematik und Ihrer Grenzgebiete |series=Neue Folge | mr=0094466 | year=1958 | volume=19| isbn=978-0-387-03123-1 }} ...

...eihMuwkh4DsC | publisher=[[Springer-Verlag]] | location=Berlin, New York | series=Ergebnisse der Mathematik und ihrer Grenzgebiete. Neue Folge. | mr=0094466 ...emic Press Inc. [Harcourt Brace Jovanovich Publishers] | location=London | series=Pure and Applied Mathematics | isbn=978-0-12-594380-2 | mr=741185 | year=19 ...

...space of [[test function]]s. They are closely related to [[formal Laurent series]], but are not required to have finitely many negative powers. In particula ...<math>n</math> variables <math>z_1, \cdots, z_n</math>''' is an arbitrary series ...

...on of the [[Generalized hypergeometric function|generalized hypergeometric series]], introduced by [[Joseph Kampé de Fériet]]. *[[Appell series]] ...

...eihMuwkh4DsC | publisher=[[Springer-Verlag]] | location=Berlin, New York | series=Ergebnisse der Mathematik und ihrer Grenzgebiete. Neue Folge. | mr=0094466 ...emic Press Inc. [Harcourt Brace Jovanovich Publishers] | location=London | series=Pure and Applied Mathematics | isbn=978-0-12-594380-2 | mr=741185 | year=19 ...

...eihMuwkh4DsC | publisher=[[Springer-Verlag]] | location=Berlin, New York | series=Ergebnisse der Mathematik und ihrer Grenzgebiete. Neue Folge. | mr=0094466 ...emic Press Inc. [Harcourt Brace Jovanovich Publishers] | location=London | series=Pure and Applied Mathematics | isbn=978-0-12-594380-2 | mr=741185 | year=19 ...

...eihMuwkh4DsC | publisher=[[Springer-Verlag]] | location=Berlin, New York | series=Ergebnisse der Mathematik und ihrer Grenzgebiete. Neue Folge. | mr=0094466 ...Society | year=1910 | journal=Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character | issn=0950-1 ...

{{Short description|Fourier series type expansion}} ...the general theory of summability, with application to Fourier's and other series. Quarterly Journal, 43, 1-52.</ref> The real-valued function <math>f(x)</ma ...

==Asymptotic expansions== ...ef>{{cite journal | last=Müller | first=Harald J. W. | title=On Asymptotic Expansions of Ellipsoidal Wave Functions | journal=Mathematische Nachrichten | publish ...

...dal wave functions can be expanded as a series of Legendre functions. Such expansions have been considered by Müller.<ref>H.J.W. Müller, ''Asymptotische Entwickl ...rly for prolate spheroidal wave functions.<ref>H.J.W. Müller, ''Asymptotic Expansions of Prolate Speroidal Wave Functions and their Characteristic Numbers'', J. ...

=== Borel's theorem on power series expansions === If <math>P</math> is an arbitrary [[formal power series]] in <math>n</math> indeterminates with complex coefficients then there exi ...

...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 ...