DLMF:13.10.E10 (Q4469): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q10770 / rank
 
Normal rank
Property / Symbols used: Q10770 / qualifier
 
test:

d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}

\diff{\NVar{x}}
Property / Symbols used: Q10770 / qualifier
 
xml-id: C1.S4.SS4.m1aidec

Latest revision as of 15:01, 2 January 2020

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DLMF:13.10.E10
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    Statements

    test
    ∫ 0 ∞ t λ - 1 ⁢ 𝐌 ⁡ ( a , b , - t ) ⁢ d t = Γ ⁡ ( λ ) ⁢ Γ ⁡ ( a - λ ) Γ ⁡ ( a ) ⁢ Γ ⁡ ( b - λ ) , superscript subscript 0 superscript 𝑡 𝜆 1 Kummer-confluent-hypergeometric-bold-M 𝑎 𝑏 𝑡 𝑡 Euler-Gamma 𝜆 Euler-Gamma 𝑎 𝜆 Euler-Gamma 𝑎 Euler-Gamma 𝑏 𝜆 {\displaystyle{\displaystyle\int_{0}^{\infty}t^{\lambda-1}{\mathbf{M}}\left(a,% b,-t\right)\mathrm{d}t=\frac{\Gamma\left(\lambda\right)\Gamma\left(a-\lambda% \right)}{\Gamma\left(a\right)\Gamma\left(b-\lambda\right)},}}
    0 references
    DLMF id
    DLMF:13.10.E10
    0 references
    constraint
    0 < ℜ ⁡ λ < ℜ ⁡ a 0 𝜆 𝑎 {\displaystyle{\displaystyle 0<\Re\lambda<\Re a}}
    0 references
    Symbols used
    gamma function
    test
    Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E1.m2afdec
    0 references
    Olver’s confluent hypergeometric function
    test
    𝐌 ⁡ ( a , b , z ) Kummer-confluent-hypergeometric-bold-M 𝑎 𝑏 𝑧 {\displaystyle{\displaystyle{\mathbf{M}}\left(\NVar{a},\NVar{b},\NVar{z}\right% )}}
    xml-id
    C13.S2.E3.m2afdec
    0 references
    Q10770
    test
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1aidec
    0 references
     
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