DLMF:13.4.E16 (Q4379): Difference between revisions

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‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
Property / Symbols used
 
Property / Symbols used: gamma function / rank
 
Normal rank
Property / Symbols used: gamma function / qualifier
 
Defining formula:

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.m2amdec

Revision as of 15:49, 2 January 2020

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DLMF:13.4.E16
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    Statements

    Defining formula
    𝐌 ⁡ ( a , b , - z ) = 1 2 ⁢ π ⁢ i ⁢ Γ ⁡ ( a ) ⁢ ∫ - i ⁢ ∞ i ⁢ ∞ Γ ⁡ ( a + t ) ⁢ Γ ⁡ ( - t ) Γ ⁡ ( b + t ) ⁢ z t ⁢ d t , Kummer-confluent-hypergeometric-bold-M 𝑎 𝑏 𝑧 1 2 𝜋 imaginary-unit Euler-Gamma 𝑎 superscript subscript imaginary-unit imaginary-unit Euler-Gamma 𝑎 𝑡 Euler-Gamma 𝑡 Euler-Gamma 𝑏 𝑡 superscript 𝑧 𝑡 𝑡 {\displaystyle{\displaystyle{\mathbf{M}}\left(a,b,-z\right)=\frac{1}{2\pi% \mathrm{i}\Gamma\left(a\right)}\int_{-\mathrm{i}\infty}^{\mathrm{i}\infty}% \frac{\Gamma\left(a+t\right)\Gamma\left(-t\right)}{\Gamma\left(b+t\right)}z^{t% }\mathrm{d}t,}}
    0 references
    DLMF id
    DLMF:13.4.E16
    0 references
    constraint
    | ph ⁡ z | < 1 2 ⁢ π phase 𝑧 1 2 𝜋 {\displaystyle{\displaystyle|\operatorname{ph}{z}|<\tfrac{1}{2}\pi}}
    0 references
    Symbols used
    gamma function
    Defining formula
    Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E1.m2amdec
    0 references
     
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