DLMF:13.3.E2 (Q4336)

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DLMF:13.3.E2
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    Statements

    Defining formula
    b ⁢ ( b - 1 ) ⁢ M ⁡ ( a , b - 1 , z ) + b ⁢ ( 1 - b - z ) ⁢ M ⁡ ( a , b , z ) + z ⁢ ( b - a ) ⁢ M ⁡ ( a , b + 1 , z ) = 0 , 𝑏 𝑏 1 Kummer-confluent-hypergeometric-M 𝑎 𝑏 1 𝑧 𝑏 1 𝑏 𝑧 Kummer-confluent-hypergeometric-M 𝑎 𝑏 𝑧 𝑧 𝑏 𝑎 Kummer-confluent-hypergeometric-M 𝑎 𝑏 1 𝑧 0 {\displaystyle{\displaystyle b(b-1)M\left(a,b-1,z\right)+b(1-b-z)M\left(a,b,z% \right)+z(b-a)M\left(a,b+1,z\right)=0,}}
    0 references
    DLMF id
    DLMF:13.3.E2
    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.m2aadec
    0 references
    Q11557
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C13.S1.XMD6.m1adec
    0 references
     
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