Wikipedia:WikiProject Mathematics/PlanetMath Exchange/40-XX Sequences, series, summability
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This page provides a list of all articles available at PlanetMath in the following topic:
- 40-XX Sequences, series, summability.
This list will be periodically updated. Each entry in the list has three fields:
- PM : The first field is the link to the PlanetMath article, along with the article's object ID.
- WP : The second field is either a "guessed" link to a correspondingly named Wikipedia article, produced by the script which generated the list, or one or more manually entered links to the corresponding Wikipedia articles on the subject.
- Status : The third field is the status field, which explains the current status of the entry. The recommended status entries are:
Status | means PM article |
N | not needed |
A | adequately covered |
C | copied |
M | merged |
NC | needs copying |
NM | needs merging |
- Please update the WP and Status fields as appropriate.
- if the WP field is correct please remove the qualifier "guess".
- If the corresponding Wikipedia article exists, but the link to it is wrong, please fix the link.
- If you copy or merge an article from PlanetMath, please update the WP and Status fields for that entry.
- If you have any comments, for example, thoughts on how the PlanetMath article compares to the corresponding Wikipedia article(s), please place such comments on a new indented line following the entry. Comments of this kind are very valuable.
Don't forget to include the relevant template if you copy over text or feel like an external link is warranted
- {{planetmath|id=|title=}} for copied over text
- {{planetmath reference|id=|title=}} for an external link
See the main page for examples and usage criteria.
One can use the web-based program Pmform to convert PlanetMath articles to the Wikipedia format. As a side benefit, this tool will place the PlanetMath template for you.
[edit] 40-00 General reference works (handbooks, dictionaries, bibliographies, etc.)
- PM: A prime theorem of a convergent sequence, id=6494 -- WP guess: A prime theorem of a convergent sequence -- Status: NM
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- Maybe can be merged to Cesaro mean. I don't find the PM article very valuable. Oleg Alexandrov (talk) 08:59, 10 October 2005 (UTC)
- PM: alternating series, id=2587 -- WP: alternating series -- Status: A
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- Oleg Alexandrov (talk) 08:59, 10 October 2005 (UTC)
- PM: alternating series test, id=2588 -- WP: alternating series test -- Status: A
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- Oleg Alexandrov (talk) 08:59, 10 October 2005 (UTC)
- PM: Cauchy product, id=4254 -- WP: Cauchy product -- Status: A
- Oleg Alexandrov (talk) 08:59, 10 October 2005 (UTC)
- PM: Cesáro mean, id=2725 -- WP guess: Cesáro mean -- Status: A
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- Oleg Alexandrov (talk) 08:28, 10 October 2005 (UTC)
- PM: geometric sequence, id=6238 -- WP: geometric sequence -- Status: A
- Oleg Alexandrov (talk) 08:59, 10 October 2005 (UTC)
- PM: interleave sequence, id=449 -- WP: interleave sequence -- Status: C
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- Oleg Alexandrov (talk) 08:59, 10 October 2005 (UTC)
- PM: Leibniz' estimate for alternating series, id=6523 -- WP: Leibniz' estimate for alternating series -- Status: A
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- Oleg Alexandrov (talk) 09:02, 10 October 2005 (UTC)
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- Oleg Alexandrov (talk) 08:59, 10 October 2005 (UTC)
- PM: monotonically decreasing, id=2130 -- WP: monotonically decreasing -- Status: A
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- Oleg Alexandrov (talk) 08:59, 10 October 2005 (UTC)
- PM: monotonically increasing, id=2134 -- WP: monotonically increasing -- Status: A
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- Oleg Alexandrov (talk) 08:59, 10 October 2005 (UTC)
- PM: monotonically nondecreasing, id=2136 -- WP: monotonically nondecreasing -- Status: A
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- Oleg Alexandrov (talk) 08:59, 10 October 2005 (UTC)
- PM: monotonically nonincreasing, id=2132 -- WP: monotonically nonincreasing -- Status: A
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- Oleg Alexandrov (talk) 08:59, 10 October 2005 (UTC)
- PM: remainder term, id=6522 -- WP guess: remainder term -- Status: A
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- Oleg Alexandrov (talk) 08:59, 10 October 2005 (UTC)
- PM: series, id=2973 -- WP guess: series (mathematics) -- Status: A
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- Oleg Alexandrov (talk) 08:59, 10 October 2005 (UTC)
- PM: sum of series, id=6493 -- WP: sum of series -- Status: A
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- Oleg Alexandrov (talk) 08:59, 10 October 2005 (UTC)
- PM: examples for limit comparison test, id=6893 -- WP guess: examples for limit comparison test -- Status:
- PM: examples using comparison test without limit, id=6895 -- WP guess: examples using comparison test without limit -- Status:
- PM: if \sum_{k=1}^\infty a_k converges then a_k\to 0, id=6717 -- WP guess: if \sum_k=1^\infty a_k converges then a_k\to 0 -- Status:
- PM: limit comparison test, id=6734 -- WP guess: limit comparison test -- Status:
- PM: multiplication of series, id=7431 -- WP guess: multiplication of series -- Status:
- PM: proof of limit comparison test, id=7513 -- WP guess: proof of limit comparison test -- Status:
- PM: Raabe's criteria, id=6892 -- WP guess: Raabe's criteria -- Status:
- PM: limit of sequence as sum of series, id=9858new! -- WP guess: limit of sequence as sum of series -- Status:
- PM: power tower sequence, id=8913new! -- WP guess: power tower sequence -- Status:
- PM: real part series and imaginary part series, id=9854new! -- WP guess: real part series and imaginary part series -- Status:
- PM: uncountable sums of positive numbers, id=7698new! -- WP guess: uncountable sums of positive numbers -- Status:
[edit] 40A05 Convergence and divergence of series and sequences
- PM: Abel's lemma, id=3843 -- WP guess: Abel's lemma -- Status:
- PM: absolute convergence theorem, id=4372 -- WP guess: absolute convergence theorem -- Status:
- PM: Baroni's theorem, id=4141 -- WP guess: Baroni's theorem -- Status:
- PM: Cauchy criterion for convergence, id=3894 -- WP guess: Cauchy's convergence test -- Status: C
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- See also Series (mathematics)#Convergence tests - AdamSmithee 11:10, 12 January 2006 (UTC)
- Done AdamSmithee 11:58, 16 January 2006 (UTC)
- PM: Cauchy's root test, id=3337 -- WP: Cauchy's root test -- Status: NM
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What if C=1AdamSmithee 11:10, 12 January 2006 (UTC)
- PM: comparison test, id=3889 -- WP: comparison test -- Status: A
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- AdamSmithee 11:10, 12 January 2006 (UTC)
- PM: convergent sequence, id=601 -- WP: convergent sequence -- Status: A
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- AdamSmithee 11:10, 12 January 2006 (UTC)
- PM: d'Alembert criterion for convergence, id=6502 -- WP guess: d'Alembert criterion for convergence -- Status:
- PM: determining series convergence, id=3958 -- WP guess: Series (mathematics)#Convergence tests -- Status: NM
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- PM has better wording and structure and more tests AdamSmithee 15:11, 12 January 2006 (UTC)
- PM: Dirichlet's convergence test, id=3844 -- WP guess: Dirichlet's convergence test -- Status: NC
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- See also Series (mathematics)#Convergence tests - AdamSmithee 11:10, 12 January 2006 (UTC)
- PM: example of integral test, id=4253 -- WP: integral test -- Status: NM
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- This or a more simple example AdamSmithee 11:10, 12 January 2006 (UTC)
- PM: geometric series, id=1188 -- WP: geometric series -- Status: A
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- AdamSmithee 11:10, 12 January 2006 (UTC)
- PM: harmonic series, id=3449 -- WP: harmonic series -- Status: NM
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- AdamSmithee 11:10, 12 January 2006 (UTC)
- PM: integral test, id=2590 -- WP: integral test -- Status: A
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- AdamSmithee 11:10, 12 January 2006 (UTC)
- PM: proof of Abel's lemma (by induction), id=4283 -- WP guess: proof of Abel's lemma (by induction) -- Status:
- PM: proof of Abel's test for convergence, id=3845 -- WP guess: proof of Abel's test for convergence -- Status:
- PM: proof of absolute convergence theorem, id=4373 -- WP guess: proof of absolute convergence theorem -- Status:
- PM: proof of alternating series test, id=2936 -- WP guess: proof of alternating series test -- Status:
- PM: Proof of Baroni's theorem, id=4142 -- WP guess: Proof of Baroni's theorem -- Status:
- PM: proof of Cauchy's root test, id=3934 -- WP: Cauchy's root test -- Status: M
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- AdamSmithee 11:58, 16 January 2006 (UTC)
- PM: proof of comparison test, id=3895 -- WP guess: proof of comparison test -- Status:
- PM: proof of integral test, id=4131 -- WP guess: proof of integral test -- Status:
- PM: proof of Leibniz's theorem (using Dirichlet's convergence test), id=3900 -- WP guess: proof of Leibniz's theorem (using Dirichlet's convergence test) -- Status:
- PM: Proof of Stolz-Cesaro theorem, id=3795 -- WP guess: Proof of Stolz-Cesaro theorem -- Status:
- PM: sequentially compact, id=3159 -- WP guess: sequentially compact -- Status:
- PM: Stolz-Cesaro theorem, id=3774 -- WP: Stolz-Cesaro theorem -- Status: C
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- Oleg Alexandrov (talk) 09:17, 10 October 2005 (UTC)
- PM: telescoping sum, id=5929 -- WP guess: telescoping sum -- Status:
- PM: p test, id=6894 -- WP guess: p test -- Status:
- PM: almost convergent, id=7356 -- WP guess: almost convergent -- Status:
- PM: Banach limit, id=7213 -- WP guess: Banach limit -- Status:
- PM: characterization of convergence of sequences in metric spaces, id=6832 -- WP guess: characterization of convergence of sequences in metric spaces -- Status:
- PM: example using Stolz-Cesaro theorem, id=7386 -- WP guess: example using Stolz-Cesaro theorem -- Status:
- PM: non-existence of universal series convergence criterion, id=6887 -- WP guess: non-existence of universal series convergence criterion -- Status:
- PM: proof of divergence of harmonic series, id=6890 -- WP guess: proof of divergence of harmonic series -- Status:
- PM: proof of slower divergent series, id=6891 -- WP guess: proof of slower divergent series -- Status:
- PM: slower convergent series, id=6884 -- WP guess: slower convergent series -- Status:
- PM: slower divergent series, id=6885 -- WP guess: slower divergent series -- Status:
- PM: unconditional convergence, id=7358 -- WP guess: unconditional convergence -- Status:
- PM: arithmetic series, id=8420new! -- WP guess: arithmetic series -- Status:
- PM: example of summation by parts, id=9849new! -- WP guess: example of summation by parts -- Status:
- PM: example of telescoping sum, id=9838new! -- WP guess: example of telescoping sum -- Status:
- PM: partial summation, id=8632new! -- WP guess: partial summation -- Status:
- PM: proof of Abel lemma (by expansion), id=9856new! -- WP guess: proof of Abel lemma (by expansion) -- Status:
- PM: silver ratio, id=8917new! -- WP guess: silver ratio -- Status:
- PM: silver rectangle, id=8918new! -- WP guess: silver rectangle -- Status:
[edit] 40A10 Convergence and divergence of integrals
- PM: improper integral, id=2732 -- WP guess: improper integral -- Status:
- PM: Wallis formulae, id=3294 -- WP guess: Wallis formulae -- Status:
[edit] 40A20 Convergence and divergence of infinite products
[edit] 40A25 Approximation to limiting values (summation of series, etc.)
- PM: Euler's constant, id=1883 -- WP guess: Euler's constant -- Status:
- PM: integral representations of the Mascheroni constant, id=7891new! -- WP guess: integral representations of the Mascheroni constant -- Status:
- PM: proof that Euler's constant exists, id=8771new! -- WP guess: proof that Euler's constant exists -- Status:
[edit] 40A30 Convergence and divergence of series and sequences of functions
- PM: Abel's limit theorem, id=3331 -- WP guess: Abel's limit theorem -- Status:
- PM: converges uniformly, id=4986 -- WP guess: converges uniformly -- Status:
- PM: Loewner ordering, id=6272 -- WP guess: Loewner ordering -- Status:
- PM: Löwner partial ordering, id=4206 -- WP guess: Löwner partial ordering -- Status:
- PM: Löwner's theorem, id=4201 -- WP guess: Löwner's theorem -- Status:
- PM: matrix monotone, id=4204 -- WP guess: matrix monotone -- Status:
- PM: operator monotone, id=4205 -- WP guess: operator monotone -- Status:
- PM: pointwise convergence, id=3737 -- WP guess: pointwise convergence -- Status:
- PM: proof of Abel's limit theorem, id=5583 -- WP guess: proof of Abel's limit theorem -- Status:
- PM: uniform convergence, id=3700 -- WP guess: uniform convergence -- Status:
- PM: limit laws for uniform convergence, id=7215 -- WP guess: limit laws for uniform convergence -- Status:
- PM: proof of composition limit law for uniform convergence, id=7216 -- WP guess: proof of composition limit law for uniform convergence -- Status:
- PM: the limit of a uniformly convergent sequence of continuous functions is continuous, id=7191 -- WP guess: the limit of a uniformly convergent sequence of continuous functions is continuous -- Status:
- PM: point preventing uniform convergence, id=9837new! -- WP guess: point preventing uniform convergence -- Status:
- PM: uniform convergence on union interval, id=9834new! -- WP guess: uniform convergence on union interval -- Status:
[edit] 40Axx Convergence and divergence of infinite limiting processes
[edit] 40B05 Multiple sequences and series
- PM: proof of Silverman-Toeplitz theorem, id=6533 -- WP guess: proof of Silverman-Toeplitz theorem -- Status: N
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- Oleg Alexandrov (talk) 09:03, 10 October 2005 (UTC)
- PM: Silverman-Toeplitz theorem, id=6531 -- WP: Silverman-Toeplitz theorem -- Status: A
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- Oleg Alexandrov (talk) 09:03, 10 October 2005 (UTC)
[edit] 40C99 Miscellaneous
- PM: arithmetic-geometric series, id=8087new! -- WP guess: arithmetic-geometric series -- Status:
[edit] 40Cxx General summability methods
[edit] 40D05 General theorems
[edit] 40Dxx Direct theorems on summability
[edit] 40G05 Cesáro, Euler, Nörlund and Hausdorff methods
- PM: Cesáro summability, id=3547 -- WP guess: Cesáro summability -- Status:
[edit] 40G10 Abel, Borel and power series methods
- PM: Abel summability, id=3549 -- WP guess: Abel summability -- Status:
- PM: proof of Abel's convergence theorem, id=3562 -- WP guess: proof of Abel's convergence theorem -- Status:
- PM: proof of Tauber's convergence theorem, id=3576 -- WP guess: proof of Tauber's convergence theorem -- Status: