Gasper–Rahman q-analog

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1: 17.7 Special Cases of Higher ${}_r{}^{}\varphi _s^{}$ Functions

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Gasper–Rahman $q$-Analog of Watson’s ${}_3{}^{}F_2^{}$ Sum

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Gasper–Rahman $q$-Analog of Whipple’s ${}_3{}^{}F_2^{}$ Sum

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Gasper–Rahman $q$-Analogs of the Karlsson–Minton Sums

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2: 17.1 Special Notation

§17.1 Special Notation

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$k,j,m,n,r,s$	nonnegative integers.
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►The main functions treated in this chapter are the basic hypergeometric (or $q$-hypergeometric) function ${}_r{}^{}\varphi _s^{}(a_1,a_2,\mathrm{\dots },a_r;b_1,b_2,\mathrm{\dots },b_s;q,z)$, the bilateral basic hypergeometric (or bilateral $q$-hypergeometric) function ${}_r{}^{}\psi _s^{}(a_1,a_2,\mathrm{\dots },a_r;b_1,b_2,\mathrm{\dots },b_s;q,z)$, and the $q$-analogs of the Appell functions ${\mathrm{\Phi }}^{(1)}(a;b,b^{\prime };c;q;x,y)$, ${\mathrm{\Phi }}^{(2)}(a;b,b^{\prime };c,c^{\prime };q;x,y)$, ${\mathrm{\Phi }}^{(3)}(a,a^{\prime };b,b^{\prime };c;q;x,y)$, and ${\mathrm{\Phi }}^{(4)}(a,b;c,c^{\prime };q;x,y)$. … ►These notations agree with Gasper and Rahman (2004). …

3: 17.6 ${}_2{}^{}\varphi _1^{}$ Function

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$q$-Gauss Sum

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First $q$-Chu–Vandermonde Sum

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Second $q$-Chu–Vandermonde Sum

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Bailey–Daum $q$-Kummer Sum

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$q$-Differential Equation

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4: 17.9 Further Transformations of ${}_{r+1}{}^{}\varphi _r^{}$ Functions

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F. H. Jackson’s Transformations

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$q$-Sheppard Identity

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Watson’s $q$-Analog of Whipple’s Theorem

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Gasper’s $q$-Analog of Clausen’s Formula (16.12.2)

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