DLMF:16.17.E1 (Q5277)

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DLMF:16.17.E1
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    Statements

    Defining formula
    G p , q m , n ⁡ ( z ; 𝐚 ; 𝐛 ) = G p , q m , n ⁡ ( z ; a 1 , … , a p b 1 , … , b q ) = 1 2 ⁢ π ⁢ i ⁢ ∫ L ( ∏ ℓ = 1 m Γ ⁡ ( b ℓ - s ) ⁢ ∏ ℓ = 1 n Γ ⁡ ( 1 - a ℓ + s ) / ( ∏ ℓ = m q - 1 Γ ⁡ ( 1 - b ℓ + 1 + s ) ⁢ ∏ ℓ = n p - 1 Γ ⁡ ( a ℓ + 1 - s ) ) ) ⁢ z s ⁢ d s , Meijer-G 𝑚 𝑛 𝑝 𝑞 𝑧 𝐚 𝐛 Meijer-G 𝑚 𝑛 𝑝 𝑞 𝑧 subscript 𝑎 1 … subscript 𝑎 𝑝 subscript 𝑏 1 … subscript 𝑏 𝑞 1 2 𝜋 imaginary-unit subscript 𝐿 superscript subscript product ℓ 1 𝑚 Euler-Gamma subscript 𝑏 ℓ 𝑠 superscript subscript product ℓ 1 𝑛 Euler-Gamma 1 subscript 𝑎 ℓ 𝑠 superscript subscript product ℓ 𝑚 𝑞 1 Euler-Gamma 1 subscript 𝑏 ℓ 1 𝑠 superscript subscript product ℓ 𝑛 𝑝 1 Euler-Gamma subscript 𝑎 ℓ 1 𝑠 superscript 𝑧 𝑠 𝑠 {\displaystyle{\displaystyle{G^{m,n}_{p,q}}\left(z;\mathbf{a};\mathbf{b}\right% )={G^{m,n}_{p,q}}\left(z;{a_{1},\dots,a_{p}\atop b_{1},\dots,b_{q}}\right)=% \frac{1}{2\pi\mathrm{i}}\int_{L}\left({\textstyle\ifrac{\prod\limits_{\ell=1}^% {m}\Gamma\left(b_{\ell}-s\right)\prod\limits_{\ell=1}^{n}\Gamma\left(1-a_{\ell% }+s\right)}{\left(\prod\limits_{\ell=m}^{q-1}\Gamma\left(1-b_{\ell+1}+s\right)% \prod\limits_{\ell=n}^{p-1}\Gamma\left(a_{\ell+1}-s\right)\right)}}\right)z^{s% }\mathrm{d}s,}}
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    DLMF id
    DLMF:16.17.E1
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