DLMF:16.11.E8 (Q5242)

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DLMF:16.11.E8
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    Statements

    Defining formula
    ( ∏ ℓ = 1 q - 1 Γ ⁡ ( a ℓ ) / ∏ ℓ = 1 q Γ ⁡ ( b ℓ ) ) ⁢ F q q - 1 ⁡ ( a 1 , … , a q - 1 b 1 , … , b q ; - z ) ∼ H q - 1 , q ⁢ ( z ) + E q - 1 , q ⁢ ( z ⁢ e - π ⁢ i ) + E q - 1 , q ⁢ ( z ⁢ e π ⁢ i ) , asymptotic-expansion superscript subscript product ℓ 1 𝑞 1 Euler-Gamma subscript 𝑎 ℓ superscript subscript product ℓ 1 𝑞 Euler-Gamma subscript 𝑏 ℓ Gauss-hypergeometric-pFq 𝑞 1 𝑞 subscript 𝑎 1 … subscript 𝑎 𝑞 1 subscript 𝑏 1 … subscript 𝑏 𝑞 𝑧 subscript 𝐻 𝑞 1 𝑞 𝑧 subscript 𝐸 𝑞 1 𝑞 𝑧 superscript 𝑒 𝜋 imaginary-unit subscript 𝐸 𝑞 1 𝑞 𝑧 superscript 𝑒 𝜋 imaginary-unit {\displaystyle{\displaystyle\left({\textstyle\ifrac{\prod\limits_{\ell=1}^{q-1% }\Gamma\left(a_{\ell}\right)}{\prod\limits_{\ell=1}^{q}\Gamma\left(b_{\ell}% \right)}}\right){{}_{q-1}F_{q}}\left({a_{1},\dots,a_{q-1}\atop b_{1},\dots,b_{% q}};-z\right)\sim H_{q-1,q}(z)+E_{q-1,q}(ze^{-\pi\mathrm{i}})+E_{q-1,q}(ze^{% \pi\mathrm{i}}),}}
    0 references
    DLMF id
    DLMF:16.11.E8
    0 references
    Symbols used
    gamma function
    Defining formula
    Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E1.m2acdec
    0 references
     
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