DLMF:13.18.E17 (Q4586)

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DLMF:13.18.E17
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    Statements

    test
    W 1 2 ⁢ α + 1 2 + n , 1 2 ⁢ α ⁡ ( z ) = ( - 1 ) n ⁢ ( α + 1 ) n ⁢ M 1 2 ⁢ α + 1 2 + n , 1 2 ⁢ α ⁡ ( z ) = ( - 1 ) n ⁢ n ! ⁢ e - 1 2 ⁢ z ⁢ z 1 2 ⁢ α + 1 2 ⁢ L n ( α ) ⁡ ( z ) . Whittaker-confluent-hypergeometric-W 1 2 𝛼 1 2 𝑛 1 2 𝛼 𝑧 superscript 1 𝑛 Pochhammer 𝛼 1 𝑛 Whittaker-confluent-hypergeometric-M 1 2 𝛼 1 2 𝑛 1 2 𝛼 𝑧 superscript 1 𝑛 𝑛 superscript 𝑒 1 2 𝑧 superscript 𝑧 1 2 𝛼 1 2 Laguerre-polynomial-L 𝛼 𝑛 𝑧 {\displaystyle{\displaystyle W_{\frac{1}{2}\alpha+\frac{1}{2}+n,\frac{1}{2}% \alpha}\left(z\right)=(-1)^{n}{\left(\alpha+1\right)_{n}}M_{\frac{1}{2}\alpha+% \frac{1}{2}+n,\frac{1}{2}\alpha}\left(z\right)=(-1)^{n}n!e^{-\frac{1}{2}z}z^{% \frac{1}{2}\alpha+\frac{1}{2}}L^{(\alpha)}_{n}\left(z\right).}}
    0 references
    DLMF id
    DLMF:13.18.E17
    0 references
    Symbols used
    Q11333
    test
    L n ( α ) ⁡ ( x ) Laguerre-polynomial-L 𝛼 𝑛 𝑥 {\displaystyle{\displaystyle L^{(\NVar{\alpha})}_{\NVar{n}}\left(\NVar{x}% \right)}}
    xml-id
    C18.S3.T1.t1.r12.m2adec
    0 references
     
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