DLMF:13.10.E5 (Q4464): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q10811 / rank
 
Normal rank
Property / Symbols used: Q10811 / qualifier
 
Defining formula:

ℜ ⁡ absent {\displaystyle{\displaystyle\Re}}

\realpart@@
Property / Symbols used: Q10811 / qualifier
 
xml-id: C1.S9.E2.m1abdec

Latest revision as of 16:01, 2 January 2020

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DLMF:13.10.E5
No description defined

    Statements

    Defining formula
    ∫ 0 ∞ e - t ⁢ t b - 1 ⁢ 𝐌 ⁡ ( a , c , t ) ⁢ d t = Γ ⁡ ( b ) ⁢ Γ ⁡ ( c - a - b ) Γ ⁡ ( c - a ) ⁢ Γ ⁡ ( c - b ) , superscript subscript 0 superscript 𝑒 𝑡 superscript 𝑡 𝑏 1 Kummer-confluent-hypergeometric-bold-M 𝑎 𝑐 𝑡 𝑡 Euler-Gamma 𝑏 Euler-Gamma 𝑐 𝑎 𝑏 Euler-Gamma 𝑐 𝑎 Euler-Gamma 𝑐 𝑏 {\displaystyle{\displaystyle\int_{0}^{\infty}e^{-t}t^{b-1}{\mathbf{M}}\left(a,% c,t\right)\mathrm{d}t=\frac{\Gamma\left(b\right)\Gamma\left(c-a-b\right)}{% \Gamma\left(c-a\right)\Gamma\left(c-b\right)},}}
    0 references
    DLMF id
    DLMF:13.10.E5
    0 references
    constraint
    ℜ ⁡ ( c - a ) > ℜ ⁡ b > 0 𝑐 𝑎 𝑏 0 {\displaystyle{\displaystyle\Re(c-a)>\Re b>0}}
    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.m2aadec
    0 references
    Olver’s confluent hypergeometric function
    Defining formula
    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.m2acdec
    0 references
    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1addec
    0 references
    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2abdec
    0 references
    Q10771
    Defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3addec
    0 references
    Q10811
    Defining formula
    ℜ ⁡ absent {\displaystyle{\displaystyle\Re}}
    xml-id
    C1.S9.E2.m1abdec
    0 references
     
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