DLMF:15.6.E2 (Q5040): Difference between revisions

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Property / constraint
 

c - b ≠ 1 , 2 , 3 , … 𝑐 𝑏 1 2 3 … {\displaystyle{\displaystyle c-b\neq 1,2,3,\dots}}

c-b\neq 1,2,3,\dots
Property / constraint: c - b ≠ 1 , 2 , 3 , … 𝑐 𝑏 1 2 3 … {\displaystyle{\displaystyle c-b\neq 1,2,3,\dots}} / rank
 
Normal rank

Revision as of 16:54, 30 December 2019

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DLMF:15.6.E2
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    Statements

    test
    𝐅 ⁡ ( a , b ; c ; z ) = Γ ⁡ ( 1 + b - c ) 2 ⁢ π ⁢ i ⁢ Γ ⁡ ( b ) ⁢ ∫ 0 ( 1 + ) t b - 1 ⁢ ( t - 1 ) c - b - 1 ( 1 - z ⁢ t ) a ⁢ d t , scaled-hypergeometric-bold-F 𝑎 𝑏 𝑐 𝑧 Euler-Gamma 1 𝑏 𝑐 2 𝜋 imaginary-unit Euler-Gamma 𝑏 superscript subscript 0 limit-from 1 superscript 𝑡 𝑏 1 superscript 𝑡 1 𝑐 𝑏 1 superscript 1 𝑧 𝑡 𝑎 𝑡 {\displaystyle{\displaystyle\mathbf{F}\left(a,b;c;z\right)=\frac{\Gamma\left(1% +b-c\right)}{2\pi\mathrm{i}\Gamma\left(b\right)}\int_{0}^{(1+)}\frac{t^{b-1}(t% -1)^{c-b-1}}{(1-zt)^{a}}\mathrm{d}t,}}
    0 references
    DLMF id
    DLMF:15.6.E2
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    constraint
    | ph ⁡ ( 1 - z ) | < π phase 1 𝑧 {\displaystyle{\displaystyle|\operatorname{ph}\left(1-z\right)|<\pi}}
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    ℜ ⁡ b > 0 𝑏 0 {\displaystyle{\displaystyle\Re b>0}}
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    | ph ⁡ ( 1 - z ) | < π ph 1 𝑧 𝜋 {\displaystyle{\displaystyle|\operatorname{ph}\left(1-z\right)|<\pi}}
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    c - b ≠ 1 , 2 , 3 , … 𝑐 𝑏 1 2 3 … {\displaystyle{\displaystyle c-b\neq 1,2,3,\dots}}
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