DLMF:12.7.E13 (Q4136)

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DLMF:12.7.E13
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    Statements

    Defining formula
    u 2 ⁢ ( a , z ) = z ⁢ e - 1 4 ⁢ z 2 ⁢ M ⁡ ( 1 2 ⁢ a + 3 4 , 3 2 , 1 2 ⁢ z 2 ) = z ⁢ e 1 4 ⁢ z 2 ⁢ M ⁡ ( - 1 2 ⁢ a + 3 4 , 3 2 , - 1 2 ⁢ z 2 ) . subscript 𝑢 2 𝑎 𝑧 𝑧 superscript 𝑒 1 4 superscript 𝑧 2 Kummer-confluent-hypergeometric-M 1 2 𝑎 3 4 3 2 1 2 superscript 𝑧 2 𝑧 superscript 𝑒 1 4 superscript 𝑧 2 Kummer-confluent-hypergeometric-M 1 2 𝑎 3 4 3 2 1 2 superscript 𝑧 2 {\displaystyle{\displaystyle u_{2}(a,z)=ze^{-\tfrac{1}{4}z^{2}}M\left(\tfrac{1% }{2}a+\tfrac{3}{4},\tfrac{3}{2},\tfrac{1}{2}z^{2}\right)=ze^{\tfrac{1}{4}z^{2}% }M\left(-\tfrac{1}{2}a+\tfrac{3}{4},\tfrac{3}{2},-\tfrac{1}{2}z^{2}\right).}}
    0 references
    DLMF id
    DLMF:12.7.E13
    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
     
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