1. 40: Sequences, Series, Summability 40B05 Multiple sequences and series (should also be assigned at least one otherclassification number in this section); 40C General summability methods; 40D http://www.math.niu.edu/~rusin/known-math/index/40-XX.html

Search Subject Index MathMap Tour ... Help! ABOUT: Introduction History Related areas Subfields POINTERS: Texts Software Web links Selected topics here 40: Sequences, series, summability Introduction Sequences and series are really just the most common examples of limiting processes; convergence criteria and rates of convergence are as important as finding "the answer". (In the case of sequences of functions, it's also important do find "the question"!) Particular series of interest (e.g. Taylor series of known functions) are of interest, as well as general methods for computing sums rapidly, or formally. Series can be estimated with integrals, their stability can be investigated with analysis. Manipulations of series (e.g. multiplying or inverting) are also of importance. History Applications and related fields Sequences are discussed here, but for sequences of integers and their number-theoretic properties, see number theory Finite trigonometric sums are treated in 11L: Exponential sums and character sums The general question of whether or not a function defined by a series can be evaluated simply in terms of "known" functions is delicate; by analogy with differential equations, it is possible to deduce some answers using the tools of 12H: Differential and difference algebra Subfields Convergence and divergence of infinite limiting processes Multiple sequences and series (should also be assigned at least one other classification number in this section) General summability methods Direct theorems on summability

2. 40-XX Prev 39 Up Top Next 41 . sequences, series, summability. 4000 http://www.rzuser.uni-heidelberg.de/~d19/msc/40.htm

40-XX Top Sequences, series, summability General reference works (handbooks, dictionaries, bibliographies, etc.) Instructional exposition (textbooks, tutorial papers, etc.) Research exposition (monographs, survey articles) Historical (must also be assigned at least one classification number from Section 01) Explicit machine computation and programs (not the theory of computation or programming) Proceedings, conferences, collections, etc. Convergence and divergence of infinite limiting processes Convergence and divergence of series and sequences Convergence and divergence of integrals Convergence and divergence of continued fractions [See also ] [xref: 11A55, 30B70] Convergence and divergence of infinite products Approximation to limiting values (summation of series, etc.) Convergence and divergence of series and sequences of functions None of the above, but in this section Multiple sequences and series General summability methods Matrix methods Integral methods Function-theoretic methods (including power series methods and semicontinuous methods) None of the above, but in this section

3. 40 Sequences, Series, Summability Settheoretic characteristics of summability of sequences and convergence of series. 281 (1987), pp. 173 183. http://www.math.ethz.ch/EMIS/journals/CMUC/cmucinde/cams-40.htm

Bhagchandani L.K., Mehra K.N. A Saalschutzian theorem for triple series . 10:2 (1969), pp. 319 322. Bor H. . 32:3 (1991), pp. 435 439. Cassens P., Regan F. On generalized Lambert summability . 11:4 (1970), pp. 829 839. Set-theoretic characteristics of summability of sequences and convergence of series . 28:1 (1987), pp. 173 183. More on set-theoretic characteristics of summability of sequences by regular (Toeplitz) matrices . 29:1 (1988), pp. 97 102.

4. KLUWER Academic Publishers | Sequences, Series, Summability summability of MultiDimensional Fourier series and Hardy Spaces Ferenc Weisz March2002, ISBN 1-4020-0564-4, Hardbound Price 112.00 EUR / 103.00 USD / 71.00 http://www.wkap.nl/home/topics/J/5/C/

Title Authors Affiliation ISBN ISSN advanced search search tips Home Browse by Subject ... Analysis Sequences, Series, Summability Sort listing by: A-Z Z-A Publication Date Analytic and Elementary Number Theory Krishnaswami Alladi, P.D.T.A. Elliott, A. Granville, G. Tenenbaum September 1998, ISBN 0-7923-8273-0, Hardbound Price: 152.00 EUR / 192.00 USD / 115.50 GBP Add to cart Applications of Fibonacci Numbers, Volume 3 Gerald E. Bergum, Andreas N. Philippou, Alwyn F. Horadam December 1989, ISBN 0-7923-0523-X, Hardbound Price: 215.00 EUR / 272.50 USD / 164.50 GBP Add to cart Asymptotic Behaviour of Linearly Transformed Sums of Random Variables Valery V. Buldygin, Serguei Solntsev June 1997, ISBN 0-7923-4632-7, Hardbound Price: 275.00 EUR / 347.00 USD / 209.50 GBP Add to cart Asymptotics of Linear Differential Equations M.H. Lantsman September 2001, ISBN 0-7923-7193-3, Hardbound Price: 181.50 EUR / 167.00 USD / 114.50 GBP Add to cart Bifurcations and Periodic Orbits of Vector Fields Dana Schlomiuk July 1993, ISBN 0-7923-2392-0, Hardbound Printing on Demand Price: 303.00 EUR / 383.50 USD / 231.00 GBP

5. The Math Forum - Math Library - Sequences/Series Title Authors Affiliation ISBN ISSN advanced search search tips Books » summability of MultiDimensional Fourier series and Hardy Spaces summability of Multi-Dimensional Fourier series and Hardy Spaces Add to cart by Ferenc Weisz Dept. Numerical http://mathforum.com/library/topics/sequence_series

Browse and Search the Library Home Math Topics Calculus (SV) : Sequences/Series Library Home Search Full Table of Contents Suggest a Link ... Library Help Selected Sites (see also All Sites in this category Sequence and Series (calculus@internet) - WebPrimitives, Cambridge, Massachusetts Links to Web pages for resources for sequences and series in calculus. more>> Sequences, Series, Summability - Dave Rusin; The Mathematical Atlas A short article designed to provide an introduction to sequences and series, the most common examples of limiting processes; convergence criteria and rates of convergence are as important as finding "the answer." Particular series of interest (e.g. Taylor series of known functions) are of interest, as well as general methods for computing sums rapidly, or formally. Series can be estimated with integrals, their stability can be investigated with analysis. Manipulations of series (e.g. multiplying or inverting) are also of importance. History; applications and related fields and subfields; textbooks, reference works, and tutorials; software and tables; other web sites with this focus. more>> All Sites - 24 items found, showing 1 to 24

6. KLUWER Academic Publishers | Sequences, Series, Summability summability of MultiDimensional Fourier series and Hardy Spaces Ferenc Weisz March2002, ISBN 1-4020-0564-4, Hardbound Price 112.00 EUR / 103.00 USD / 71.00 http://www.wkap.nl/home/topics/J/5/C/?sort=P&results=0

7. About "Sequences, Series, Summability" sequences, series, summability. Library Home Full Table of Contents Suggest a Link Library Help Visit this site http//www http://mathforum.org/library/view/7601.html

Sequences, Series, Summability Library Home Full Table of Contents Suggest a Link Library Help Visit this site: http://www.math.niu.edu/~rusin/known-math/index/40-XX.html Author: Dave Rusin; The Mathematical Atlas Description: A short article designed to provide an introduction to sequences and series, the most common examples of limiting processes; convergence criteria and rates of convergence are as important as finding "the answer." Particular series of interest (e.g. Taylor series of known functions) are of interest, as well as general methods for computing sums rapidly, or formally. Series can be estimated with integrals, their stability can be investigated with analysis. Manipulations of series (e.g. multiplying or inverting) are also of importance. History; applications and related fields and subfields; textbooks, reference works, and tutorials; software and tables; other web sites with this focus. Levels: College Languages: English Resource Types: Articles Math Topics: Sequences and Series Suggestion Box Home The Math Library ... Search http://mathforum.org/ webmaster@mathforum.org

8. Mhdl40.htm 40XX. sequences, series, summability. 40-00. General reference works (handbooks, dictionaries, bibliographies, etc.) http://www.math.unipd.it/~biblio/math/doppiaeng/mhdl40.htm

40-XX Sequences, series, summability General reference works (handbooks, dictionaries, bibliographies, etc.) Instructional exposition (textbooks, tutorial papers, etc.) Research exposition (monographs, survey articles) Explicit machine computation and programs (not the theory of computation or programming) Proceedings, conferences, collections, etc. Convergence and divergence of infinite limiting processes Convergence and divergence of series and sequences Convergence and divergence of integrals Convergence and divergence of continued fractions [See also Convergence and divergence of infinite products Convergence and divergence of series and sequences of functions None of the above, but in this section General summability methods Matrix methods Integral methods Function-theoretic methods (including power series methods and semicontinuous methods) None of the above, but in this section Direct theorems on summability General theorems Structure of summability fields Tauberian constants and oscillation limits Convergence factors and summability factors Summability and bounded fields of methods Inclusion and equivalence theorems None of the above, but in this section

9. The Math Forum - Math Library - Sequences/Series sequences, series, summability Dave Rusin; The Mathematical Atlas A short articledesigned to provide an introduction to sequences and series, the most http://mathforum.org/library/topics/sequence_series/

Browse and Search the Library Home Math Topics Calculus (SV) : Sequences/Series Library Home Search Full Table of Contents Suggest a Link ... Library Help Selected Sites (see also All Sites in this category Sequence and Series (calculus@internet) - WebPrimitives, Cambridge, Massachusetts Links to Web pages for resources for sequences and series in calculus. more>> Sequences, Series, Summability - Dave Rusin; The Mathematical Atlas A short article designed to provide an introduction to sequences and series, the most common examples of limiting processes; convergence criteria and rates of convergence are as important as finding "the answer." Particular series of interest (e.g. Taylor series of known functions) are of interest, as well as general methods for computing sums rapidly, or formally. Series can be estimated with integrals, their stability can be investigated with analysis. Manipulations of series (e.g. multiplying or inverting) are also of importance. History; applications and related fields and subfields; textbooks, reference works, and tutorials; software and tables; other web sites with this focus. more>> All Sites - 24 items found, showing 1 to 24

10. PlanetMath: Harmonic Series AMS MSC 40A05 (sequences, series, summability Convergence and divergence of infinite limiting processes http://www.planetmath.org/encyclopedia/PSeries.html

Math for the people, by the people. Encyclopedia Books Papers Expositions ... Random Login create new user name: pass: forget your password? Main Menu the math Encyclop¦dia Papers Books Expositions meta Requests Orphanage Unclass'd Unproven ... Corrections talkback Polls Forums Feedback Bug Reports information Docs Classification News Legalese ... TODO List harmonic series (Definition) The harmonic series is The harmonic series is known to diverge. This can be proven via the integral test ; compare with A harmonic series is any series of the form These are the so-called "p-series." When , these are known to converge (leading to the p-series test for series convergence). For complex-valued , the Riemann zeta function A famous harmonic series is (or ), which converges to . In general no -harmonic series of odd has been solved analytically. A harmonic series which is not summed to , but instead is of the form is called a harmonic series of order of "harmonic series" is owned by akrowne view preamble View style: HTML with images page images TeX source See Also: harmonic number Also defines: p-series, harmonic series of order

11. 40 Sequences, Series, Summability 114 (1970), pp. 829 839. Vojt\'a\v{s} P. Settheoretic characteristics of summabilityof sequences and convergence of series. 281 (1987), pp. 173 183. http://www.emis.de/journals/CMUC/cmucinde/cams-40.htm

Bhagchandani L.K., Mehra K.N. A Saalschutzian theorem for triple series . 10:2 (1969), pp. 319 322. Bor H. . 32:3 (1991), pp. 435 439. Cassens P., Regan F. On generalized Lambert summability . 11:4 (1970), pp. 829 839. Set-theoretic characteristics of summability of sequences and convergence of series . 28:1 (1987), pp. 173 183. More on set-theoretic characteristics of summability of sequences by regular (Toeplitz) matrices . 29:1 (1988), pp. 97 102.

12. PlanetMath: Power Series variable series expansions Power series). 40A30 (sequences, series, summability Convergence and divergence http://www.planetmath.org/encyclopedia/PowerSeries.html

Math for the people, by the people. Encyclopedia Books Papers Expositions ... Random Login create new user name: pass: forget your password? Main Menu the math Encyclop¦dia Papers Books Expositions meta Requests Orphanage Unclass'd Unproven ... Corrections talkback Polls Forums Feedback Bug Reports information Docs Classification News Legalese ... TODO List power series (Definition) A power series is a function of the form with or . The are called the coefficients and the center of the power series. Every power series is convergent at least at where it converges to . In addition it is absolutely convergent in the region , with It is divergent for every with . For no general predictions can be made. If , the power series converges absolutely for every real or complex The real number is called the radius of convergence of the power series. Examples of power series are: Taylor series , for example: The geometric series with "power series" is owned by mathwizard full author list view preamble View style: HTML with images page images TeX source See Also: Taylor series formal power series Cross-references: geometric series Taylor series radius of convergence complex ... function There are 15 references to this object.

13. Subject Index Of CMUC 1 (1960) - 35 (1994) differential equations; 35 Partial differential equations; 40 sequences,series, summability; 41 Approximation and expansion; 42 Fourier http://www.emis.de/journals/CMUC/cmucinde/cams6094.htm

Subject index of CMUC 1 (1960) - 35 (1994) General Mathematical logic and foundations Set theory Combinatorics ... Information and communication, circuits

14. 40-XX 40XX sequences, series, summability. 40-00 General reference works (handbooks, dictionaries, bibliographies, etc.) http://www-mathdoc.ujf-grenoble.fr/MSC1991/40-XX.html

40-XX Sequences, series, summability 40-00 General reference works (handbooks, dictionaries, bibliographies, etc.) 40-01 Instructional exposition (textbooks, tutorial papers, etc.) 40-02 Research exposition (monographs, survey articles) 40-03 Historical (must be assigned at least one classification number from 01-XX 40-04 Explicit machine computation and programs (not the theory of computation or programming) 40-06 Proceedings, conferences, collections, etc. 40Axx Convergence and divergence of infinite limiting processes 40Cxx General summability methods 40Dxx Direct theorems on summability 40Exx Inversion theorems 40F05 Absolute and strong summability 40Gxx Special methods of summability 40H05 Functional analytic methods in summability Top level of Index

15. 40Xxx - Sequences, Series, Summability 40Xxx sequences, series, summability 40Axx Convergence anddivergence of infinite limiting processes 40A05 , Convergence http://jipam.vu.edu.au/subj_classf/40Xxx.htm

[40Xxx] Sequences, series, summability Convergence and divergence of infinite limiting processes Convergence and divergence of series and sequences Convergence and divergence of continued fractions Direct theorems on summability Convergence factors and summability factors ] Absolute and strong summability ] Summability in abstract structures Editors R.P. Agarwal G. Anastassiou T. Ando H. Araki A.G. Babenko D. Bainov N.S. Barnett H. Bor J. Borwein P.S. Bullen P. Cerone S.H. Cheng L. Debnath S.S. Dragomir N. Elezovic A.M. Fink A. Fiorenza T. Furuta L. Gajek H. Gauchman C. Giordano F. Hansen D. Hinton A. Laforgia L. Leindler C.-K. Li L. Losonczi A. Lupas R. Mathias T. Mills G.V. Milovanovic R.N. Mohapatra B. Mond M.Z. Nashed C.P. Niculescu I. Olkin B. Opic B. Pachpatte Z. Pales C.E.M. Pearce J. Pecaric L.-E. Persson L. Pick I. Pressman S. Puntanen F. Qi A.G. Ramm T.M. Rassias A. Rubinov S. Saitoh J. Sandor S.P. Singh A. Sofo H.M. Srivastava K.B. Stolarsky G.P.H. Styan L. Toth

16. Sequences, Series, Summability sequences, series, summability. 40Axx Convergence and divergence ofinfinite limiting processes. 40B05 Multiple sequences and series. http://www.iwr.uni-heidelberg.de/groups/compalg/gruber/WWW/40-XXmon.html

Sequences, series, summability 40Axx Convergence and divergence of infinite limiting processes 40B05 Multiple sequences and series 40Cxx General summability methods 40Dxx Direct theorems on summability 40Exx Inversion theorems includes 40F05 Absolute and strong summability 40Gxx Special methods of summability 40H05 Functional analytic methods in summability 40J05 Summability in abstract structures

17. 40-XX 40XX sequences, series, summability. 40-00 General reference works (handbooks,dictionaries, bibliographies, etc.); 40-01 Instructional http://www.ams.org/mathweb/msc1991/40-XX.html

40-XX Sequences, series, summability 40-00 General reference works (handbooks, dictionaries, bibliographies, etc.) 40-01 Instructional exposition (textbooks, tutorial papers, etc.) 40-02 Research exposition (monographs, survey articles) 40-03 Historical (must be assigned at least one classification number from Section 01) 40-04 Explicit machine computation and programs (not the theory of computation or programming) 40-06 Proceedings, conferences, collections, etc. Convergence and divergence of infinite limiting processes General summability methods Direct theorems on summability Inversion theorems 40F05 Absolute and strong summability Special methods of summability 40H05 Functional analytic methods in summability 40J05 Summability in abstract structures [See also Top level of Index

18. 40-xx 40xx, Prev 39 Up Top Next 41 . sequences, series, summability.40-00 General reference works (handbooks, dictionaries, bibliographies http://www.ams.org/msc/40-xx.html

40-xx Top Sequences, series, summability 40-00 General reference works (handbooks, dictionaries, bibliographies, etc.) 40-01 Instructional exposition (textbooks, tutorial papers, etc.) 40-02 Research exposition (monographs, survey articles) 40-03 Historical (must also be assigned at least one classification number from Section 01) 40-04 Explicit machine computation and programs (not the theory of computation or programming) 40-06 Proceedings, conferences, collections, etc. Convergence and divergence of infinite limiting processes General summability methods Direct theorems on summability Inversion theorems 40F05 Absolute and strong summability Special methods of summability 40H05 Functional analytic methods in summability 40J05 Summability in abstract structures [See also

19. MSC91 40XX sequences, series, summability ( 0 Dok.). 40-00 General referenceworks (handbooks, dictionaries, bibliographies, etc.) ( 0 Dok.); http://elib.uni-stuttgart.de/opus/msc_ebene2.php?zahl=40&anzahl=0

20. MSC91 Konstanz Konstanzer OnlinePublikations-System. Mathematics SubjectClassification 1991. 40-XX sequences, series, summability ( 0 Dok.). http://www.ub.uni-konstanz.de/cgi-bin/w3-msql/v13/msc_ebene2.html?zahl=40&anzahl

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