DLMF:7.18.E10 (Q2460)

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DLMF:7.18.E10
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    Statements

    Defining formula
    i n ⁢ erfc ⁡ ( z ) = e - z 2 2 n ⁢ π ⁢ U ⁡ ( 1 2 ⁢ n + 1 2 , 1 2 , z 2 ) . repeated-integral-complementary-error-function 𝑛 𝑧 superscript 𝑒 superscript 𝑧 2 superscript 2 𝑛 𝜋 Kummer-confluent-hypergeometric-U 1 2 𝑛 1 2 1 2 superscript 𝑧 2 {\displaystyle{\displaystyle\mathop{\mathrm{i}^{n}\mathrm{erfc}}\left(z\right)% =\frac{e^{-z^{2}}}{2^{n}\sqrt{\pi}}U\left(\tfrac{1}{2}n+\tfrac{1}{2},\tfrac{1}% {2},z^{2}\right).}}
    0 references
    DLMF id
    DLMF:7.18.E10
    0 references
    Symbols used
    Kummer confluent hypergeometric function
    Defining formula
    U ⁡ ( a , b , z ) Kummer-confluent-hypergeometric-U 𝑎 𝑏 𝑧 {\displaystyle{\displaystyle U\left(\NVar{a},\NVar{b},\NVar{z}\right)}}
    xml-id
    C13.S2.E6.m2adec
    0 references
     
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