DLMF:13.4.E1 (Q4364)

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DLMF:13.4.E1
No description defined

    Statements

    test
    𝐌 ⁑ ( a , b , z ) = 1 Ξ“ ⁑ ( a ) ⁒ Ξ“ ⁑ ( b - a ) ⁒ ∫ 0 1 e z ⁒ t ⁒ t a - 1 ⁒ ( 1 - t ) b - a - 1 ⁒ d t , Kummer-confluent-hypergeometric-bold-M π‘Ž 𝑏 𝑧 1 Euler-Gamma π‘Ž Euler-Gamma 𝑏 π‘Ž superscript subscript 0 1 superscript 𝑒 𝑧 𝑑 superscript 𝑑 π‘Ž 1 superscript 1 𝑑 𝑏 π‘Ž 1 𝑑 {\displaystyle{\displaystyle{\mathbf{M}}\left(a,b,z\right)=\frac{1}{\Gamma% \left(a\right)\Gamma\left(b-a\right)}\int_{0}^{1}e^{zt}t^{a-1}(1-t)^{b-a-1}% \mathrm{d}t,}}
    0 references
    DLMF id
    DLMF:13.4.E1
    0 references
    constraint
    β„œ ⁑ b > β„œ ⁑ a > 0 𝑏 π‘Ž 0 {\displaystyle{\displaystyle\Re b>\Re a>0}}
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    Symbols used
    gamma function
    test
    Ξ“ ⁑ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E1.m2adec
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    Olver’s confluent hypergeometric function
    test
    𝐌 ⁑ ( a , b , z ) Kummer-confluent-hypergeometric-bold-M π‘Ž 𝑏 𝑧 {\displaystyle{\displaystyle{\mathbf{M}}\left(\NVar{a},\NVar{b},\NVar{z}\right% )}}
    xml-id
    C13.S2.E3.m2adec
    0 references
    Q10770
    test
    d x π‘₯ {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1adec
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    base of natural logarithm
    test
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2adec
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    Q10771
    test
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3adec
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    Q10811
    test
    β„œ ⁑ absent {\displaystyle{\displaystyle\Re}}
    xml-id
    C1.S9.E2.m1adec
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    Q11557
    test
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C13.S1.XMD6.m1dec
    0 references
     
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