DLMF:13.3.E5 (Q4339)

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DLMF:13.3.E5
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    Statements

    Defining formula
    b ⁢ ( a + z ) ⁢ M ⁡ ( a , b , z ) + z ⁢ ( a - b ) ⁢ M ⁡ ( a , b + 1 , z ) - a ⁢ b ⁢ M ⁡ ( a + 1 , b , z ) = 0 , 𝑏 𝑎 𝑧 Kummer-confluent-hypergeometric-M 𝑎 𝑏 𝑧 𝑧 𝑎 𝑏 Kummer-confluent-hypergeometric-M 𝑎 𝑏 1 𝑧 𝑎 𝑏 Kummer-confluent-hypergeometric-M 𝑎 1 𝑏 𝑧 0 {\displaystyle{\displaystyle b(a+z)M\left(a,b,z\right)+z(a-b)M\left(a,b+1,z% \right)-abM\left(a+1,b,z\right)=0,}}
    0 references
    DLMF id
    DLMF:13.3.E5
    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.m2addec
    0 references
    Q11557
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C13.S1.XMD6.m1ddec
    0 references
     
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