DLMF:15.6.E5 (Q5043): Difference between revisions

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Property / constraint
 

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

b,c-b\neq 1,2,3,\dots
Property / constraint: b , c - b ≠ 1 , 2 , 3 , … formulae-sequence 𝑏 𝑐 𝑏 1 2 3 … {\displaystyle{\displaystyle b,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.E5
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    Statements

    test
    𝐅 ⁡ ( a , b ; c ; z ) = e - c ⁢ π ⁢ i ⁢ Γ ⁡ ( 1 - b ) ⁢ Γ ⁡ ( 1 + b - c ) ⁢ 1 4 ⁢ π 2 ⁢ ∫ A ( 0 + , 1 + , 0 - , 1 - ) t b - 1 ⁢ ( 1 - t ) c - b - 1 ( 1 - z ⁢ t ) a ⁢ d t , scaled-hypergeometric-bold-F 𝑎 𝑏 𝑐 𝑧 superscript 𝑒 𝑐 𝜋 imaginary-unit Euler-Gamma 1 𝑏 Euler-Gamma 1 𝑏 𝑐 1 4 superscript 𝜋 2 superscript subscript 𝐴 limit-from 0 limit-from 1 limit-from 0 limit-from 1 superscript 𝑡 𝑏 1 superscript 1 𝑡 𝑐 𝑏 1 superscript 1 𝑧 𝑡 𝑎 𝑡 {\displaystyle{\displaystyle\mathbf{F}\left(a,b;c;z\right)=e^{-c\pi\mathrm{i}}% \Gamma\left(1-b\right)\Gamma\left(1+b-c\right)\*\frac{1}{4\pi^{2}}\int_{A}^{(0% +,1+,0-,1-)}\frac{t^{b-1}(1-t)^{c-b-1}}{(1-zt)^{a}}\mathrm{d}t,}}
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    DLMF id
    DLMF:15.6.E5
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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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    | ph ⁡ ( 1 - z ) | < π ph 1 𝑧 𝜋 {\displaystyle{\displaystyle|\operatorname{ph}\left(1-z\right)|<\pi}}
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    b , c - b ≠ 1 , 2 , 3 , … formulae-sequence 𝑏 𝑐 𝑏 1 2 3 … {\displaystyle{\displaystyle b,c-b\neq 1,2,3,\dots}}
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