DLMF:12.14.E16 (Q4256)

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DLMF:12.14.E16
No description defined

    Statements

    Defining formula
    w 2 ⁢ ( a , x ) = x ⁢ e - 1 4 ⁢ i ⁢ x 2 ⁢ M ⁡ ( 3 4 - 1 2 ⁢ i ⁢ a , 3 2 , 1 2 ⁢ i ⁢ x 2 ) = x ⁢ e 1 4 ⁢ i ⁢ x 2 ⁢ M ⁡ ( 3 4 + 1 2 ⁢ i ⁢ a , 3 2 , - 1 2 ⁢ i ⁢ x 2 ) . subscript 𝑤 2 𝑎 𝑥 𝑥 superscript 𝑒 1 4 𝑖 superscript 𝑥 2 Kummer-confluent-hypergeometric-M 3 4 1 2 𝑖 𝑎 3 2 1 2 𝑖 superscript 𝑥 2 𝑥 superscript 𝑒 1 4 𝑖 superscript 𝑥 2 Kummer-confluent-hypergeometric-M 3 4 1 2 𝑖 𝑎 3 2 1 2 𝑖 superscript 𝑥 2 {\displaystyle{\displaystyle w_{2}(a,x)=xe^{-\frac{1}{4}ix^{2}}M\left(\tfrac{3% }{4}-\tfrac{1}{2}ia,\tfrac{3}{2},\tfrac{1}{2}ix^{2}\right)=xe^{\frac{1}{4}ix^{% 2}}M\left(\tfrac{3}{4}+\tfrac{1}{2}ia,\tfrac{3}{2},-\tfrac{1}{2}ix^{2}\right).}}
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    DLMF id
    DLMF:12.14.E16
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    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
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    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2acdec
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    imaginary unit
    Defining formula
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2aedec
    0 references
    Q11520
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C12.S1.XMD1.m1ldec
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    Q11516
    Defining formula
    a 𝑎 {\displaystyle{\displaystyle a}}
    xml-id
    C12.S1.XMD6.m1ldec
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    odd solution (locally)
    Defining formula
    w 2 ⁢ ( a , x ) subscript 𝑤 2 𝑎 𝑥 {\displaystyle{\displaystyle w_{2}(a,x)}}
    xml-id
    C12.S14.XMD5.m1bdec
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