Formula:KLS:01.10:08

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