DLMF:13.4.E2 (Q4365)

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DLMF:13.4.E2
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    Statements

    test
    𝐌 ⁑ ( a , b , z ) = 1 Ξ“ ⁑ ( b - c ) ⁒ ∫ 0 1 𝐌 ⁑ ( a , c , z ⁒ t ) ⁒ t c - 1 ⁒ ( 1 - t ) b - c - 1 ⁒ d t , Kummer-confluent-hypergeometric-bold-M π‘Ž 𝑏 𝑧 1 Euler-Gamma 𝑏 𝑐 superscript subscript 0 1 Kummer-confluent-hypergeometric-bold-M π‘Ž 𝑐 𝑧 𝑑 superscript 𝑑 𝑐 1 superscript 1 𝑑 𝑏 𝑐 1 𝑑 {\displaystyle{\displaystyle{\mathbf{M}}\left(a,b,z\right)=\frac{1}{\Gamma% \left(b-c\right)}\int_{0}^{1}{\mathbf{M}}\left(a,c,zt\right)t^{c-1}(1-t)^{b-c-% 1}\mathrm{d}t,}}
    0 references
    DLMF id
    DLMF:13.4.E2
    0 references
    constraint
    β„œ ⁑ b > β„œ ⁑ c > 0 𝑏 𝑐 0 {\displaystyle{\displaystyle\Re b>\Re c>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.m2aadec
    0 references
    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.m2aadec
    0 references
    Q10770
    test
    d x π‘₯ {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1aadec
    0 references
     
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