Formula:KLS:01.10:06: Difference between revisions

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Latest revision as of 08:33, 22 December 2019


lim a r \qHyperrphis r s @ @ a 1 , , a r b 1 , , b s q z a r = \qHyperrphis r - 1 s @ @ a 1 , , a r - 1 b 1 , , b s q z formulae-sequence subscript subscript 𝑎 𝑟 \qHyperrphis 𝑟 𝑠 @ @ subscript 𝑎 1 subscript 𝑎 𝑟 subscript 𝑏 1 subscript 𝑏 𝑠 𝑞 𝑧 subscript 𝑎 𝑟 \qHyperrphis 𝑟 1 𝑠 @ @ subscript 𝑎 1 subscript 𝑎 𝑟 1 subscript 𝑏 1 subscript 𝑏 𝑠 𝑞 𝑧 {\displaystyle{\displaystyle{\displaystyle\lim\limits_{a_{r}\rightarrow\infty}% \qHyperrphis{r}{s}@@{a_{1},\ldots,a_{r}}{b_{1},\ldots,b_{s}}{q}{\frac{z}{a_{r}% }}=\qHyperrphis{r-1}{s}@@{a_{1},\ldots,a_{r-1}}{b_{1},\ldots,b_{s}}{q}{z}}}}

Proof

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Symbols List

ϕ s r subscript subscript italic-ϕ 𝑠 𝑟 {\displaystyle{\displaystyle{\displaystyle{{}_{r}\phi_{s}}}}}  : basic hypergeometric (or q 𝑞 {\displaystyle{\displaystyle{\displaystyle q}}} -hypergeometric) function : http://dlmf.nist.gov/17.4#E1

Bibliography

Equation in Section 1.10 of KLS.

URL links

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