DLMF:13.21.E8 (Q4616)

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DLMF:13.21.E8
No description defined

    Statements

    Defining formula
    c ⁢ ( κ , μ ) = e μ ⁢ π ⁢ i ⁢ 1 2 ⁢ π ⁢ ( κ - μ κ + μ ) 1 2 ⁢ μ ⁢ ( e 2 κ 2 - μ 2 ) 1 2 ⁢ κ , 𝑐 𝜅 𝜇 superscript 𝑒 𝜇 𝜋 imaginary-unit 1 2 𝜋 superscript 𝜅 𝜇 𝜅 𝜇 1 2 𝜇 superscript superscript 𝑒 2 superscript 𝜅 2 superscript 𝜇 2 1 2 𝜅 {\displaystyle{\displaystyle c(\kappa,\mu)=e^{\mu\pi\mathrm{i}}\sqrt{\tfrac{1}% {2}\pi}\left(\frac{\kappa-\mu}{\kappa+\mu}\right)^{\frac{1}{2}\mu}\left(\frac{% e^{2}}{\kappa^{2}-\mu^{2}}\right)^{\frac{1}{2}\kappa},}}
    0 references
    DLMF id
    DLMF:13.21.E8
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    Symbols used
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2addec
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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.m2abdec
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