DLMF:15.8.E13 (Q5070): 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.E13
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    Statements

    test
    F ⁡ ( a , b 2 ⁢ b ; z ) = ( 1 - 1 2 ⁢ z ) - a ⁢ F ⁡ ( 1 2 ⁢ a , 1 2 ⁢ a + 1 2 b + 1 2 ; ( z 2 - z ) 2 ) , Gauss-hypergeometric-F 𝑎 𝑏 2 𝑏 𝑧 superscript 1 1 2 𝑧 𝑎 Gauss-hypergeometric-F 1 2 𝑎 1 2 𝑎 1 2 𝑏 1 2 superscript 𝑧 2 𝑧 2 {\displaystyle{\displaystyle F\left({a,b\atop 2b};z\right)=\left(1-\tfrac{1}{2% }z\right)^{-a}F\left({\tfrac{1}{2}a,\tfrac{1}{2}a+\tfrac{1}{2}\atop b+\tfrac{1% }{2}};\left(\frac{z}{2-z}\right)^{2}\right),}}
    0 references
    DLMF id
    DLMF:15.8.E13
    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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