DLMF:14.20.E20 (Q4941)

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DLMF:14.20.E20
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    Statements

    Defining formula
    σ ⁢ ( μ , τ ) = exp ⁡ ( μ - τ ⁢ arctan ⁡ α ) ( μ 2 + τ 2 ) μ / 2 . 𝜎 𝜇 𝜏 𝜇 𝜏 𝛼 superscript superscript 𝜇 2 superscript 𝜏 2 𝜇 2 {\displaystyle{\displaystyle\sigma(\mu,\tau)=\frac{\exp\left(\mu-\tau% \operatorname{arctan}\alpha\right)}{\left(\mu^{2}+\tau^{2}\right)^{\mu/2}}.}}
    0 references
    DLMF id
    DLMF:14.20.E20
    0 references
    Symbols used
    exponential function
    Defining formula
    exp ⁡ z 𝑧 {\displaystyle{\displaystyle\exp\NVar{z}}}
    xml-id
    C4.S2.E19.m2adec
    0 references
    Q10816
    Defining formula
    arctan ⁡ z 𝑧 {\displaystyle{\displaystyle\operatorname{arctan}\NVar{z}}}
    xml-id
    C4.S23.SS2.p1.m7adec
    0 references
    Q11630
    Defining formula
    τ 𝜏 {\displaystyle{\displaystyle\tau}}
    xml-id
    C14.S1.XMD3.m1aadec
    0 references
    Q11591
    Defining formula
    μ 𝜇 {\displaystyle{\displaystyle\mu}}
    xml-id
    C14.S1.XMD7.m1odec
    0 references
    Q11633
    Defining formula
    α 𝛼 {\displaystyle{\displaystyle\alpha}}
    xml-id
    C14.S20.XMD5.m1cdec
    0 references
    Q11634
    Defining formula
    σ ⁢ ( μ , τ ) 𝜎 𝜇 𝜏 {\displaystyle{\displaystyle\sigma(\mu,\tau)}}
    xml-id
    C14.S20.XMD6.m1bdec
    0 references
     
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