Formula:KLS:01.10:09

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

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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