Talk:Quantum calculus

I could find very little on the subject! hopefully someone else can elaborate Robbjedi 05:30, 18 October 2005 (UTC)

Is this in any way similar to Heim's "Selector Calculus"? 67.128.168.14 22:33, 25 February 2006 (UTC)Don Granberry.

Dimentional value cannot be an exponent!!!!! 77.126.245.189 (talk) 18:12, 14 October 2013 (UTC)

Can you explain more clearly what you mean? At present, I have no idea what that means. JamesBWatson (talk) 20:25, 15 October 2013 (UTC)

Numerous Issues

Much of this article appears to be a poorly rewritten version of Kac and Cheung (2002) that is also riddled with inaccuracies. For example, the current revision of the article (as of March 24, 2024) gives the relation $q=e^{ih}$ and states that $h$ is Planck's constant. Kac and Cheung states that they are "usually related by $q=e^{h}$" and that "the letter $h$ is used as a reminder of Planck's constant" (4), rather than actually being Planck's constant.

In a slightly different vein, it would appear that the 'Example' section's discussion of the q-derivative and h-derivative's "niceness" is a poorly written rewording of Kac and Cheung's statement that "It is fair to say that $x^{n}$ is a good function in q-calculus but a bad one in h-calculus." (2-3). Additionally, Kac and Cheung make no mention of the falling factorial, and I can find no relation that agrees with the current revision's claim that the h-analog of $x^{n}$ is the falling factorial.

The 'History' section also appears to be a poorly re-worded version of the introduction in Kac and Cheung.

I have added 'No footnotes' and 'Copy editing' as issues with this article, as only one source is actually cited, and Kac and Cheung is only given as a reference, rather than being properly cited. Aquikos (talk) 06:29, 24 March 2024 (UTC)

Some potential sources for more information on this topic include:

• Thomas Ernst's A Comprehensive Treatment of q-Calculus (2012)
• Thomas Ernst's The History of q-Calculus and a New Method (2000)
• New q-derivative and q-logarithm (Chung et. al, 1994)

Gasper and Rahman (2004) is listed under Further Reading, but could be used as a source for more information on this subject.

The History section of this article should likely make note of some of the contributions made by the following individuals (this list was largely compiled from information given in Ernst (2000)):

• F. H. Jackson for the introduction of the q-derivative and (general) q-integral in On q-functions and a certain and a certain difference operator (1908) and On q-integrals (1910)
• Eduard Heine for the introduction of the q-hypergeometric series
• Euler for the q-exponential function
• Cauchy for the first proof of the q-binomial theorem (it appears that the formula was introduced but was not proven by Ferd Schweins in his 1820 work Analysis, but I am insufficiently proficient in German to read that work.)
• Gauss for the q-binomial formula

Aquikos (talk) 19:17, 24 March 2024 (UTC)

Removal of h-calculus

The only source that is listed, and indeed that I am able to find at all, for the existence of h-calculus is Kac and Cheung (2002). This work primarily focuses on q-calculus, but appears to also serve as an introduction of terminology for h-calculus. This is not inherently a problem, but I cannot find any other works that adopt this terminology and it is explicitly stated that h-calculus is simply the calculus of finite differences. They also explicitly state that: "the h-Taylor formula is nothing else but Newton's interpolation formula, and h-integration by parts is simply the Abel transform." (pg. viii) It is for this reason that I suggest that mentions of h-calculus be removed from this page and possibly moved to Finite difference or a related page. While its applications are likely quite useful, it seems out of place in this article. Aquikos (talk) 19:26, 24 March 2024 (UTC)