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DLMF:13.2.E4 - MaRDI portal

DLMF:13.2.E4 (Q4991)

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DLMF:13.2.E4
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    Statements

    DLMF defining formula
    M ⁑ ( a , b , z ) = Ξ“ ⁑ ( b ) ⁒ 𝐌 ⁑ ( a , b , z ) . Kummer-confluent-hypergeometric-M π‘Ž 𝑏 𝑧 Euler-Gamma 𝑏 Kummer-confluent-hypergeometric-bold-M π‘Ž 𝑏 𝑧 {\displaystyle{\displaystyle M\left(a,b,z\right)=\Gamma\left(b\right){\mathbf{% M}}\left(a,b,z\right).}}
    0 references
    Symbols used
    gamma function
    DLMF defining formula
    Ξ“ ⁑ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E1.m2aadec
    0 references
    $$={{}_{1}F_{1}}\left(\NVar{a};\NVar{b};\NVar{z}\right)$$ Kummer confluent hypergeometric function
    DLMF defining formula
    M ⁑ ( a , b , z ) Kummer-confluent-hypergeometric-M π‘Ž 𝑏 𝑧 {\displaystyle{\displaystyle M\left(\NVar{a},\NVar{b},\NVar{z}\right)}}
    xml-id
    C13.S2.E2.m2aadec
    0 references
    Olver’s confluent hypergeometric function
    DLMF defining formula
    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
    complex variable
    DLMF defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C13.S1.XMD6.m1cdec
    0 references

    Identifiers

     
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