DLMF:13.4.E2 (Q4365): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q11557 / rank
 
Normal rank
Property / Symbols used: Q11557 / qualifier
 
test:

z 𝑧 {\displaystyle{\displaystyle z}}

z
Property / Symbols used: Q11557 / qualifier
 
xml-id: C13.S1.XMD6.m1adec
Property / Symbols used
 
Property / Symbols used: Q11562 / rank
 
Normal rank
Property / Symbols used: Q11562 / qualifier
 
test:

c 𝑐 {\displaystyle{\displaystyle c}}

c
Property / Symbols used: Q11562 / qualifier
 
xml-id: C13.S4.XMD1.m1dec

Latest revision as of 14:45, 2 January 2020

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DLMF:13.4.E2
No description defined

    Statements

    test
    𝐌 ⁡ ( a , b , z ) = 1 Γ ⁡ ( b - c ) ⁢ ∫ 0 1 𝐌 ⁡ ( a , c , z ⁢ t ) ⁢ t c - 1 ⁢ ( 1 - t ) b - c - 1 ⁢ d t , Kummer-confluent-hypergeometric-bold-M 𝑎 𝑏 𝑧 1 Euler-Gamma 𝑏 𝑐 superscript subscript 0 1 Kummer-confluent-hypergeometric-bold-M 𝑎 𝑐 𝑧 𝑡 superscript 𝑡 𝑐 1 superscript 1 𝑡 𝑏 𝑐 1 𝑡 {\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
    ℜ ⁡ b > ℜ ⁡ c > 0 𝑏 𝑐 0 {\displaystyle{\displaystyle\Re b>\Re c>0}}
    0 references
    Symbols used
    gamma function
    test
    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
    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.m2aadec
    0 references
    Q10770
    test
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1aadec
    0 references
    Q10771
    test
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3aadec
    0 references
    Q10811
    test
    ℜ ⁡ absent {\displaystyle{\displaystyle\Re}}
    xml-id
    C1.S9.E2.m1aadec
    0 references
    Q11557
    test
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C13.S1.XMD6.m1adec
    0 references
    Q11562
    test
    c 𝑐 {\displaystyle{\displaystyle c}}
    xml-id
    C13.S4.XMD1.m1dec
    0 references
     
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