Wiki143:WikiProject Mathematics/PlanetMath Exchange/40-XX Sequences, series, summability

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

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

Oleg Alexandrov (talk) 08:59, 10 October 2005 (UTC)

• PM: alternating series test, id=2588 -- WP: alternating series test -- Status: A

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

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

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

Oleg Alexandrov (talk) 09:02, 10 October 2005 (UTC)

• PM: monotonic, id=2141 -- WP: monotonic -- Status: A

Oleg Alexandrov (talk) 08:59, 10 October 2005 (UTC)

• PM: monotonically decreasing, id=2130 -- WP: monotonically decreasing -- Status: A

Oleg Alexandrov (talk) 08:59, 10 October 2005 (UTC)

• PM: monotonically increasing, id=2134 -- WP: monotonically increasing -- Status: A

Oleg Alexandrov (talk) 08:59, 10 October 2005 (UTC)

• PM: monotonically nondecreasing, id=2136 -- WP: monotonically nondecreasing -- Status: A

Oleg Alexandrov (talk) 08:59, 10 October 2005 (UTC)

• PM: monotonically nonincreasing, id=2132 -- WP: monotonically nonincreasing -- Status: A

Oleg Alexandrov (talk) 08:59, 10 October 2005 (UTC)

• PM: remainder term, id=6522 -- WP guess: remainder term -- Status: A

Oleg Alexandrov (talk) 08:59, 10 October 2005 (UTC)

• PM: series, id=2973 -- WP guess: series (mathematics) -- Status: A

Oleg Alexandrov (talk) 08:59, 10 October 2005 (UTC)

• PM: sum of series, id=6493 -- WP: sum of series -- Status: A

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=9858^new! -- WP guess: limit of sequence as sum of series -- Status:

• PM: power tower sequence, id=8913^new! -- WP guess: power tower sequence -- Status:

• PM: real part series and imaginary part series, id=9854^new! -- WP guess: real part series and imaginary part series -- Status:

• PM: uncountable sums of positive numbers, id=7698^new! -- WP guess: uncountable sums of positive numbers -- Status:

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

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

What if C=1 AdamSmithee 11:10, 12 January 2006 (UTC)

• PM: comparison test, id=3889 -- WP: comparison test -- Status: A

AdamSmithee 11:10, 12 January 2006 (UTC)

• PM: convergent sequence, id=601 -- WP: convergent sequence -- Status: A

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

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

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

This or a more simple example AdamSmithee 11:10, 12 January 2006 (UTC)

• PM: geometric series, id=1188 -- WP: geometric series -- Status: A

AdamSmithee 11:10, 12 January 2006 (UTC)

• PM: harmonic series, id=3449 -- WP: harmonic series -- Status: NM

AdamSmithee 11:10, 12 January 2006 (UTC)

• PM: integral test, id=2590 -- WP: integral test -- Status: A

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

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

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=8420^new! -- WP guess: arithmetic series -- Status:

• PM: example of summation by parts, id=9849^new! -- WP guess: example of summation by parts -- Status:

• PM: example of telescoping sum, id=9838^new! -- WP guess: example of telescoping sum -- Status:

• PM: partial summation, id=8632^new! -- WP guess: partial summation -- Status:

• PM: proof of Abel lemma (by expansion), id=9856^new! -- WP guess: proof of Abel lemma (by expansion) -- Status:

• PM: silver ratio, id=8917^new! -- WP guess: silver ratio -- Status:

• PM: silver rectangle, id=8918^new! -- WP guess: silver rectangle -- Status:

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:

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=7891^new! -- WP guess: integral representations of the Mascheroni constant -- Status:

• PM: proof that Euler's constant exists, id=8771^new! -- WP guess: proof that Euler's constant exists -- Status:

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=9837^new! -- WP guess: point preventing uniform convergence -- Status:

• PM: uniform convergence on union interval, id=9834^new! -- WP guess: uniform convergence on union interval -- Status:

40B05 Multiple sequences and series

• PM: proof of Silverman-Toeplitz theorem, id=6533 -- WP guess: proof of Silverman-Toeplitz theorem -- Status: N

Oleg Alexandrov (talk) 09:03, 10 October 2005 (UTC)

• PM: Silverman-Toeplitz theorem, id=6531 -- WP: Silverman-Toeplitz theorem -- Status: A

Oleg Alexandrov (talk) 09:03, 10 October 2005 (UTC)

40C99 Miscellaneous

• PM: arithmetic-geometric series, id=8087^new! -- WP guess: arithmetic-geometric series -- Status:

40G05 Cesáro, Euler, Nörlund and Hausdorff methods

• PM: Cesáro summability, id=3547 -- WP guess: Cesáro summability -- Status:

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: