DLMF:13.4.E10 (Q4373): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: gamma function / rank
 
Normal rank
Property / Symbols used: gamma function / qualifier
 
test:

Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}

\EulerGamma@{\NVar{z}}
Property / Symbols used: gamma function / qualifier
 
xml-id: C5.S2.E1.m2ahdec

Revision as of 14:47, 2 January 2020

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DLMF:13.4.E10
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    Statements

    test
    𝐌 ⁡ ( a , b , z ) = e - a ⁢ π ⁢ i ⁢ Γ ⁡ ( 1 - a ) 2 ⁢ π ⁢ i ⁢ Γ ⁡ ( b - a ) ⁢ ∫ 1 ( 0 + ) e z ⁢ t ⁢ t a - 1 ⁢ ( 1 - t ) b - a - 1 ⁢ d t , Kummer-confluent-hypergeometric-bold-M 𝑎 𝑏 𝑧 superscript 𝑒 𝑎 𝜋 imaginary-unit Euler-Gamma 1 𝑎 2 𝜋 imaginary-unit Euler-Gamma 𝑏 𝑎 superscript subscript 1 limit-from 0 superscript 𝑒 𝑧 𝑡 superscript 𝑡 𝑎 1 superscript 1 𝑡 𝑏 𝑎 1 𝑡 {\displaystyle{\displaystyle{\mathbf{M}}\left(a,b,z\right)=e^{-a\pi\mathrm{i}}% \frac{\Gamma\left(1-a\right)}{2\pi\mathrm{i}\Gamma\left(b-a\right)}\int_{1}^{(% 0+)}e^{zt}t^{a-1}{(1-t)^{b-a-1}}\mathrm{d}t,}}
    0 references
    DLMF id
    DLMF:13.4.E10
    0 references
    constraint
    ℜ ⁡ ( b - a ) > 0 𝑏 𝑎 0 {\displaystyle{\displaystyle\Re(b-a)>0}}
    0 references
    a ≠ 1 , 2 , 3 , … 𝑎 1 2 3 … {\displaystyle{\displaystyle a\neq 1,2,3,\dots}}
    0 references
    ℜ ⁡ ( b - a ) > 0 𝑏 𝑎 0 {\displaystyle{\displaystyle\Re(b-a)>0}}
    0 references
    Symbols used
    gamma function
    test
    Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E1.m2ahdec
    0 references
     
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