Formula:KLS:01.04:07

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

Proof

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Symbols List

F q p subscript subscript 𝐹 𝑞 𝑝 {\displaystyle{\displaystyle{\displaystyle{{}_{p}F_{q}}}}}  : generalized hypergeometric function : http://dlmf.nist.gov/16.2#E1

Bibliography

Equation in Section 1.4 of KLS.

URL links

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