DLMF:13.4.E9 (Q4372): Difference between revisions

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Property / constraint
 

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

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

Revision as of 16:45, 30 December 2019

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DLMF:13.4.E9
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    Statements

    test
    𝐌 ⁡ ( a , b , z ) = Γ ⁡ ( 1 + a - b ) 2 ⁢ π ⁢ i ⁢ Γ ⁡ ( a ) ⁢ ∫ 0 ( 1 + ) e z ⁢ t ⁢ t a - 1 ⁢ ( t - 1 ) b - a - 1 ⁢ d t , Kummer-confluent-hypergeometric-bold-M 𝑎 𝑏 𝑧 Euler-Gamma 1 𝑎 𝑏 2 𝜋 imaginary-unit Euler-Gamma 𝑎 superscript subscript 0 limit-from 1 superscript 𝑒 𝑧 𝑡 superscript 𝑡 𝑎 1 superscript 𝑡 1 𝑏 𝑎 1 𝑡 {\displaystyle{\displaystyle{\mathbf{M}}\left(a,b,z\right)=\frac{\Gamma\left(1% +a-b\right)}{2\pi\mathrm{i}\Gamma\left(a\right)}\int_{0}^{(1+)}e^{zt}t^{a-1}{(% t-1)^{b-a-1}}\mathrm{d}t,}}
    0 references
    DLMF id
    DLMF:13.4.E9
    0 references
    constraint
    ℜ ⁡ a > 0 𝑎 0 {\displaystyle{\displaystyle\Re a>0}}
    0 references
    b - a ≠ 1 , 2 , 3 , … 𝑏 𝑎 1 2 3 … {\displaystyle{\displaystyle b-a\neq 1,2,3,\dots}}
    0 references
     
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