DLMF:13.3.E6 (Q4340)

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DLMF:13.3.E6
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    Statements

    Defining formula
    ( a - 1 + z ) ⁢ M ⁡ ( a , b , z ) + ( b - a ) ⁢ M ⁡ ( a - 1 , b , z ) + ( 1 - b ) ⁢ M ⁡ ( a , b - 1 , z ) = 0 . 𝑎 1 𝑧 Kummer-confluent-hypergeometric-M 𝑎 𝑏 𝑧 𝑏 𝑎 Kummer-confluent-hypergeometric-M 𝑎 1 𝑏 𝑧 1 𝑏 Kummer-confluent-hypergeometric-M 𝑎 𝑏 1 𝑧 0 {\displaystyle{\displaystyle(a-1+z)M\left(a,b,z\right)+(b-a)M\left(a-1,b,z% \right)+(1-b)M\left(a,b-1,z\right)=0.}}
    0 references
    DLMF id
    DLMF:13.3.E6
    0 references
    Symbols used
    $$={{}_{1}F_{1}}\left(\NVar{a};\NVar{b};\NVar{z}\right)$$ Kummer confluent hypergeometric function
    Defining formula
    M ⁡ ( a , b , z ) Kummer-confluent-hypergeometric-M 𝑎 𝑏 𝑧 {\displaystyle{\displaystyle M\left(\NVar{a},\NVar{b},\NVar{z}\right)}}
    xml-id
    C13.S2.E2.m2aedec
    0 references
    Q11557
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C13.S1.XMD6.m1edec
    0 references
     
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