# Talk:Hypergeometric function

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Mathematics rating:
 C Class
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Field:  Analysis

## Pochhammer symbol

I'm not familiar to this topic, but according to this article, (q)n is defined by:

${\displaystyle (q)_{n}={\begin{cases}1&{\mbox{if }}n=0\\q\left(q-1\right)\cdots \left(q-n+1\right)&{\mbox{if }}n>0\end{cases}}}$

Jdh8 (talk) 15:16, 6 December 2012 (UTC)

Looks like a mistake. It should be the rising factorial ${\displaystyle q^{(n)}}$. This would be consistent with the definition given in the article about generalized hypergeometric function. — Preceding unsigned comment added by 141.89.116.54 (talk) 12:48, 14 February 2013 (UTC)
Yeah, don't confuse rising and falling; they're different. There are several different conventions and notations in common use, and you need to take care not to get tripped up. All of the WP articles in this area were all self-consistent with one another, last time I looked. User:Linas (talk) 06:29, 1 December 2013 (UTC)
Ok, but the problem is that Wikipedia is not consistent with itself. Just check the reference to Pochhammer symbol Jdh8 gives. 2001:718:2:1634:224:1DFF:FE13:8CBC (talk) 14:19, 26 June 2014 (UTC)

## No valid antecedent

"It is a solution of a second-order..." does not have a valid antecedent. — Preceding unsigned comment added by 98.67.106.148 (talk) 06:30, 22 September 2013 (UTC)

## Identities?

As I remember it, research into the discovery of and classification of identities remains an active topic; many algorithms have been found that can generate classes of identities, but there is no complete categorization of them all -- i.e. there is no known algo that can generate all identites. This is one of the more peculair and modern aspects of this beast, I'm surprised its not covered. User:Linas (talk) 06:27, 1 December 2013 (UTC)

## Did something get lost in this edit?

Something lost? I get that feeling, but do not know. YohanN7 (talk) 16:22, 12 October 2014 (UTC)

Nope! There were two edits that should be taken as one. My mistake. YohanN7 (talk) 16:28, 12 October 2014 (UTC)

## higher order transformations

Vidunas classified 2F1 --> 2F1 transformations. I added one example to the main page (the entry 1/2,1/3,1/8 --> 1/4,1/8,1/8 in Table 2 in his paper). To guard against typing errors, here is the example in computer-readable form so one can check it with a Maple computation:

hypergeom([1/4, 3/8], [7/8], z ) * (z^4-60*z^3+134*z^2-60*z+1)^(1/16) = hypergeom([1/48, 17/48], [7/8], (-432*z*(z-1)^2*(z+1)^8 / (z^4-60*z^3+134*z^2-60*z+1)^3) );
series(lhs(%)-rhs(%), z=0, 30); MvH (talk) 14:00, 15 April 2015 (UTC)MvH

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