Wikipedia:WikiProject Mathematics/PlanetMath Exchange/33-XX Special functions

This page provides a list of all articles available at PlanetMath in the following topic:

33-XX Special functions.

This list will be periodically updated. Each entry in the list has three fields:

1. PM : The first field is the link to the PlanetMath article, along with the article's object ID.
2. 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.
3. 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.

33-00 General reference works (handbooks, dictionaries, bibliographies, etc.)

• PM: index of special functions, id=6269 -- WP: list of mathematical functions -- Status: A

linas 21:49, 13 Mar 2005 (UTC)

33B10 Exponential and trigonometric functions

• PM: natural logarithm, id=2666 -- WP: natural logarithm -- Status: A

linas 15:54, 13 Mar 2005 (UTC)

• PM: Exact Trigonometry Tables, id=7395 -- WP: Exact Trigonometry Tables -- Status:N

Curious. linas 20:41, 5 March 2006 (UTC)

• PM: proof of angle sum identities, id=9798^new! -- WP guess: proof of angle sum identities -- Status:

• PM: trigonometry, id=6807^new! -- WP guess: trigonometry -- Status:

33B15 Gamma, beta and polygamma functions

• PM: Bohr-Mollerup theorem, id=3730 -- WP: Bohr-Mollerup theorem -- Status: A

linas 21:54, 13 Mar 2005 (UTC)

• PM: evaluation of beta function using Laplace transform, id=6206 -- WP: Beta function -- Status: NM

This article provides a derivation/proof of a result quoted in main WP math articles. As such, I believe it could be useful to copy this article, as it helps establish the correctness and consistency of WP math articles. However, one may also argue that such proofs are un-needed as long as the accuracy of WP articles remains unchallenged. linas 16:35, 26 Mar 2005 (UTC)

Its short, just merge it into beta function. linas 20:37, 5 March 2006 (UTC)

• PM: proof of Bohr-Mollerup theorem, id=6576 -- WP: Bohr-Mollerup theorem -- Status: N

This article provides a derivation/proof of a result quoted in main WP math articles. As such, I believe it could be useful to copy this article, as it helps establish the correctness and consistency of WP math articles. However, one may also argue that such proofs are un-needed as long as the accuracy of WP articles remains unchallenged. linas 16:35, 26 Mar 2005 (UTC)

Change to N. linas 20:30, 5 March 2006 (UTC)

• PM: proof of Bohr-Mollerup theorem, id=3808 -- WP: Bohr-Mollerup theorem -- Status: N

This article provides a derivation/proof of a result quoted in main WP math articles. As such, I believe it could be useful to copy this article, as it helps establish the correctness and consistency of WP math articles. However, one may also argue that such proofs are un-needed as long as the accuracy of WP articles remains unchallenged. linas 16:35, 26 Mar 2005 (UTC)

Change to N. linas 20:32, 5 March 2006 (UTC)

• PM: beta function, id=4001 -- WP: beta function -- Status: A

linas 20:25, 5 March 2006 (UTC)

• PM: alternate integral representation of beta function, id=9481^new! -- WP guess: alternate integral representation of beta function -- Status:

33B20 Incomplete beta and gamma functions (error functions, probability integral, Fresnel integrals)

• PM: error function, id=6429 -- WP: error function -- Status: A

linas 16:04, 13 Mar 2005 (UTC)

33B30 Higher logarithm functions

• PM: Lambert W function, id=2957 -- WP: Lambert W function -- Status: A

linas 22:05, 13 Mar 2005 (UTC)

33B99 Miscellaneous

• PM: natural log base, id=657 -- WP: Base of the natural logarithm -- Status: A

linas 22:03, 13 Mar 2005 (UTC)

• PM: (1 + 1/n)^n is an increasing sequence, id=7775^new! -- WP guess: (1 + 1/n)^n is an increasing sequence -- Status:

• PM: bounds for e, id=7778^new! -- WP guess: bounds for e -- Status:

• PM: proof of bounds for e, id=7779^new! -- WP guess: proof of bounds for e -- Status:

• PM: values of (1 + 1/n)^n for 0 < n < 26, id=9328^new! -- WP guess: [[values of (1 + 1/n)^n for 0 < n < 26]] -- Status:

• PM: values of \displaystyle \sum_{i = 0}^n \frac{1}{i!} for 0 < n < 26, id=9401^new! -- WP guess: [[values of \displaystyle \sum_i = 0^n \frac1i! for 0 < n < 26]] -- Status:

33C05 Classical hypergeometric functions, $ 2F 1$

• PM: hypergeometric equation, id=6409 -- WP: hypergeometric differential equation -- Status: A

linas 22:12, 13 Mar 2005 (UTC)

linas 16:52, 26 Mar 2005 (UTC)

I wrote the WP article a while ago, from scratch. linas 05:03, 22 August 2005 (UTC)

• PM: hypergeometric function, id=5983 -- WP: hypergeometric function -- Status: A

linas 16:21, 13 Mar 2005 (UTC)

• PM: integral representations of the hypergeometric function, id=6150 -- WP: Euler hypergeometric integral -- Status: A

linas 22:16, 13 Mar 2005 (UTC)

linas 16:52, 26 Mar 2005 (UTC)

linas 05:05, 22 August 2005 (UTC)

OK, the contents finally actually registered; the WP article is adequate, and the proof in the PM article didn't need to be merged. linas 17:31, 5 September 2005 (UTC)

33C10 Bessel and Airy functions, cylinder functions, $ 0F 1$

• PM: Bessel's equation, id=8774^new! -- WP guess: Bessel's equation -- Status:

33C45 Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.)

• PM: Legendre polynomial, id=6961 -- WP: Legendre polynomial -- Status: A

linas 20:22, 5 March 2006 (UTC)

33D45 Basic orthogonal polynomials and functions (Askey-Wilson polynomials, etc.)

• PM: orthogonal polynomials, id=1220 -- WP: orthogonal polynomials -- Status: A

linas 20:31, 13 Mar 2005 (UTC)

• PM: Christoffel-Darboux formula, id=8474^new! -- WP guess: Christoffel-Darboux formula -- Status:

33E05 Elliptic functions and integrals

• PM: \wp-function, id=6540 -- WP: Weierstrass elliptic function -- Status: A

linas 16:46, 13 Mar 2005 (UTC)

• PM: derivation of integral represetations of Jacobi \vartheta functions, id=6263 -- WP: Derivation of integral represetations of Jacobi theta functions -- Status: NC

This article provides a derivation/proof of a result quoted in main WP math articles. As such, I beleive it could be useful to copy this article, as it helps establish the correctness and consistency of WP math articles. However, one may also argue that such proofs are un-needed as long as the accuracy of WP articles remains unchallenged. linas 16:38, 26 Mar 2005 (UTC)

• PM: elliptic function, id=4494 -- WP: elliptic function -- Status: A

linas 16:43, 13 Mar 2005 (UTC)

• PM: elliptic integrals and Jacobi elliptic functions, id=4746 -- WP: elliptic integral and Jacobian elliptic functions -- Status: A

linas 17:13, 13 Mar 2005 (UTC)

• PM: examples of elliptic functions, id=4649 -- WP: examples of elliptic functions -- Status: N

linas 17:02, 13 Mar 2005 (UTC)

• PM: integral represetations of Jacobi \vartheta functions, id=6262 -- WP: theta function -- Status: M

linas 01:00, 14 Mar 2005 (UTC)

• PM: Jacobi \vartheta functions, id=5550 -- WP: theta function -- Status: M

linas 17:18, 13 Mar 2005 (UTC)

• PM: Jacobi's identity for \vartheta functions, id=6427 -- WP: theta functions -- Status: M

linas 00:06, 14 Mar 2005 (UTC)

• PM: modular discriminant, id=4651 -- WP: modular discriminant -- Status: A

linas 20:06, 13 Mar 2005 (UTC)

• PM: product representations of Jacobi \vartheta functions, id=6546 -- WP: theta function -- Status: M

linas 23:31, 13 Mar 2005 (UTC)

• PM: proof of Jacobi's identity for \vartheta functions, id=6434 -- WP: proof of Jacobi's identity for theta functions -- Status: NC

This article provides a derivation/proof of a result quoted in main WP math articles. As such, I beleive it could be useful to copy this article, as it helps establish the correctness and consistency of WP math articles. However, one may also argue that such proofs are un-needed as long as the accuracy of WP articles remains unchallenged. linas 16:38, 26 Mar 2005 (UTC)

• PM: Weierstrass sigma function, id=4650 -- WP: Weierstrass sigma function -- Status: C

linas 17:05, 13 Mar 2005 (UTC)

Copied it over. Ugh raw tex to html conversion was needed ugh.linas

• PM: order of an elliptic function, id=7694^new! -- WP guess: order of an elliptic function -- Status:

• PM: possible orders of elliptic functions, id=7772^new! -- WP guess: possible orders of elliptic functions -- Status:

• PM: reduction of elliptic integrals to standard form, id=8610^new! -- WP guess: reduction of elliptic integrals to standard form -- Status:

33E12 Mittag-Leffler functions and generalizations

• PM: Mittag-Leffler function, id=6594 -- WP: Mittag-Leffler function -- Status: C

linas 16:26, 13 Mar 2005 (UTC)

I just copied it over,also added the relationship to error function. linas 00:34, 14 Mar 2005 (UTC)