DLMF:2.5.E10 (Q786): Difference between revisions

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Property / constraint
 

- 2 ν < z < 1 2 𝜈 𝑧 1 {\displaystyle{\displaystyle-2\nu<\Re z<1}}

-2\nu<\realpart@@{z}<1
Property / constraint: - 2 ν < z < 1 2 𝜈 𝑧 1 {\displaystyle{\displaystyle-2\nu<\Re z<1}} / rank
 
Normal rank

Revision as of 15:52, 30 December 2019

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DLMF:2.5.E10
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    Statements

    h ( z ) = 2 z - 1 Γ ( ν + 1 2 z ) Γ 2 ( 1 - 1 2 z ) Γ ( 1 + ν - 1 2 z ) Γ ( z ) π sin ( π z ) , Mellin-transform 𝑧 superscript 2 𝑧 1 Euler-Gamma 𝜈 1 2 𝑧 Euler-Gamma 2 1 1 2 𝑧 Euler-Gamma 1 𝜈 1 2 𝑧 Euler-Gamma 𝑧 𝜋 𝜋 𝑧 {\displaystyle{\displaystyle\mathscr{M}\mskip-3.0mu h\mskip 3.0mu \left(z% \right)=\frac{2^{z-1}\Gamma\left(\nu+\frac{1}{2}z\right)}{{\Gamma^{2}}\left(1-% \frac{1}{2}z\right)\Gamma\left(1+\nu-\frac{1}{2}z\right)\Gamma\left(z\right)}% \frac{\pi}{\sin\left(\pi z\right)},}}
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    - 2 ν < z < 1 2 𝜈 𝑧 1 {\displaystyle{\displaystyle-2\nu<\Re z<1}}
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