DLMF:15.6.E9 (Q5047): Difference between revisions

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Property / constraint
 

| ph ⁡ ( 1 - z ) | < π phase 1 𝑧 {\displaystyle{\displaystyle|\operatorname{ph}\left(1-z\right)|<\pi}}

|\phase@{1-z}|<\cpi
Property / constraint: | ph ⁡ ( 1 - z ) | < π phase 1 𝑧 {\displaystyle{\displaystyle|\operatorname{ph}\left(1-z\right)|<\pi}} / rank
 
Normal rank

Revision as of 16:55, 30 December 2019

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DLMF:15.6.E9
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    Statements

    test
    𝐅 ⁡ ( a , b ; c ; z ) = ∫ 0 1 t d - 1 ⁢ ( 1 - t ) c - d - 1 ( 1 - z ⁢ t ) a + b - λ ⁢ 𝐅 ⁡ ( λ - a , λ - b d ; z ⁢ t ) ⁢ 𝐅 ⁡ ( a + b - λ , λ - d c - d ; ( 1 - t ) ⁢ z 1 - z ⁢ t ) ⁢ d t , scaled-hypergeometric-bold-F 𝑎 𝑏 𝑐 𝑧 superscript subscript 0 1 superscript 𝑡 𝑑 1 superscript 1 𝑡 𝑐 𝑑 1 superscript 1 𝑧 𝑡 𝑎 𝑏 𝜆 scaled-hypergeometric-bold-F 𝜆 𝑎 𝜆 𝑏 𝑑 𝑧 𝑡 scaled-hypergeometric-bold-F 𝑎 𝑏 𝜆 𝜆 𝑑 𝑐 𝑑 1 𝑡 𝑧 1 𝑧 𝑡 𝑡 {\displaystyle{\displaystyle\mathbf{F}\left(a,b;c;z\right)=\int_{0}^{1}\frac{t% ^{d-1}(1-t)^{c-d-1}}{(1-zt)^{a+b-\lambda}}\mathbf{F}\left({\lambda-a,\lambda-b% \atop d};zt\right)\mathbf{F}\left({a+b-\lambda,\lambda-d\atop c-d};\frac{(1-t)% z}{1-zt}\right)\mathrm{d}t,}}
    0 references
    DLMF id
    DLMF:15.6.E9
    0 references
    constraint
    | ph ⁡ ( 1 - z ) | < π phase 1 𝑧 {\displaystyle{\displaystyle|\operatorname{ph}\left(1-z\right)|<\pi}}
    0 references
     
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