DLMF:15.8.E1 (Q5058): Difference between revisions

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Property / constraint
 

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

|\phase@{1-z}|<\pi
Property / constraint: | ph ⁡ ( 1 - z ) | < π phase 1 𝑧 𝜋 {\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:15.8.E1
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    Statements

    test
    𝐅 ⁡ ( a , b c ; z ) = ( 1 - z ) - a ⁢ 𝐅 ⁡ ( a , c - b c ; z z - 1 ) = ( 1 - z ) - b ⁢ 𝐅 ⁡ ( c - a , b c ; z z - 1 ) = ( 1 - z ) c - a - b ⁢ 𝐅 ⁡ ( c - a , c - b c ; z ) , scaled-hypergeometric-bold-F 𝑎 𝑏 𝑐 𝑧 superscript 1 𝑧 𝑎 scaled-hypergeometric-bold-F 𝑎 𝑐 𝑏 𝑐 𝑧 𝑧 1 superscript 1 𝑧 𝑏 scaled-hypergeometric-bold-F 𝑐 𝑎 𝑏 𝑐 𝑧 𝑧 1 superscript 1 𝑧 𝑐 𝑎 𝑏 scaled-hypergeometric-bold-F 𝑐 𝑎 𝑐 𝑏 𝑐 𝑧 {\displaystyle{\displaystyle\mathbf{F}\left({a,b\atop c};z\right)=(1-z)^{-a}% \mathbf{F}\left({a,c-b\atop c};\frac{z}{z-1}\right)=(1-z)^{-b}\mathbf{F}\left(% {c-a,b\atop c};\frac{z}{z-1}\right)=(1-z)^{c-a-b}\mathbf{F}\left({c-a,c-b\atop c% };z\right),}}
    0 references
    DLMF id
    DLMF:15.8.E1
    0 references
    constraint
    | ph ⁡ ( 1 - z ) | < π phase 1 𝑧 𝜋 {\displaystyle{\displaystyle|\operatorname{ph}\left(1-z\right)|<\pi}}
    0 references
     
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