DLMF:12.7.E12 (Q4135)

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DLMF:12.7.E12
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    Statements

    Defining formula
    u 1 ⁢ ( a , z ) = e - 1 4 ⁢ z 2 ⁢ M ⁡ ( 1 2 ⁢ a + 1 4 , 1 2 , 1 2 ⁢ z 2 ) = e 1 4 ⁢ z 2 ⁢ M ⁡ ( - 1 2 ⁢ a + 1 4 , 1 2 , - 1 2 ⁢ z 2 ) , subscript 𝑢 1 𝑎 𝑧 superscript 𝑒 1 4 superscript 𝑧 2 Kummer-confluent-hypergeometric-M 1 2 𝑎 1 4 1 2 1 2 superscript 𝑧 2 superscript 𝑒 1 4 superscript 𝑧 2 Kummer-confluent-hypergeometric-M 1 2 𝑎 1 4 1 2 1 2 superscript 𝑧 2 {\displaystyle{\displaystyle u_{1}(a,z)=e^{-\tfrac{1}{4}z^{2}}M\left(\tfrac{1}% {2}a+\tfrac{1}{4},\tfrac{1}{2},\tfrac{1}{2}z^{2}\right)=e^{\tfrac{1}{4}z^{2}}M% \left(-\tfrac{1}{2}a+\tfrac{1}{4},\tfrac{1}{2},-\tfrac{1}{2}z^{2}\right),}}
    0 references
    DLMF id
    DLMF:12.7.E12
    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.m2adec
    0 references
     
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