Formula:KLS:01.13:28: Difference between revisions

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Latest revision as of 08:34, 22 December 2019


\qHyperrphis ⁢ 43 ⁢ @ ⁢ @ ⁢ a 2 , b 2 , c , d ⁢ a ⁢ b ⁢ q 1 / 2 , - a ⁢ b ⁢ q 1 / 2 , - c ⁢ d ⁢ q ⁢ q = \qHyperrphis ⁢ 43 ⁢ ( a 2 , b 2 , c 2 , d 2 a 2 ⁢ b 2 ⁢ q , - c ⁢ d , - c ⁢ d ⁢ q ; q 2 , q 2 ) \qHyperrphis 43 @ @ superscript 𝑎 2 superscript 𝑏 2 𝑐 𝑑 𝑎 𝑏 superscript 𝑞 1 2 𝑎 𝑏 superscript 𝑞 1 2 𝑐 𝑑 𝑞 𝑞 \qHyperrphis 43 FRACOP superscript 𝑎 2 superscript 𝑏 2 superscript 𝑐 2 superscript 𝑑 2 superscript 𝑎 2 superscript 𝑏 2 𝑞 𝑐 𝑑 𝑐 𝑑 𝑞 superscript 𝑞 2 superscript 𝑞 2 {\displaystyle{\displaystyle{\displaystyle{}{}\qHyperrphis{4}{3}@@{a^{2},b^{2}% ,c,d}{abq^{1/2},-abq^{1/2},-cd}{q}{q}=\qHyperrphis{4}{3}\left(\genfrac{}{}{0.0% pt}{}{a^{2},b^{2},c^{2},d^{2}}{a^{2}b^{2}q,-cd,-cdq}\,;\,q^{2},q^{2}\right)}}}

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 1.13 of KLS.

URL links

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