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DLMF:13.14.E10 - MaRDI portal

DLMF:13.14.E10 (Q5196)

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DLMF:13.14.E10
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    Statements

    DLMF defining formula
    M κ , μ ⁡ ( z ⁢ e ± π ⁢ i ) = ± i ⁢ e ± μ ⁢ π ⁢ i ⁢ M - κ , μ ⁡ ( z ) . Whittaker-confluent-hypergeometric-M 𝜅 𝜇 𝑧 superscript 𝑒 plus-or-minus 𝜋 imaginary-unit plus-or-minus imaginary-unit superscript 𝑒 plus-or-minus 𝜇 𝜋 imaginary-unit Whittaker-confluent-hypergeometric-M 𝜅 𝜇 𝑧 {\displaystyle{\displaystyle M_{\kappa,\mu}\left(ze^{\pm\pi\mathrm{i}}\right)=% \pm\mathrm{i}e^{\pm\mu\pi\mathrm{i}}M_{-\kappa,\mu}\left(z\right).}}
    0 references
    Symbols used
    Whittaker confluent hypergeometric function
    DLMF defining formula
    M κ , μ ⁡ ( z ) Whittaker-confluent-hypergeometric-M 𝜅 𝜇 𝑧 {\displaystyle{\displaystyle M_{\NVar{\kappa},\NVar{\mu}}\left(\NVar{z}\right)}}
    xml-id
    C13.S14.E2.m2addec
    0 references
    the ratio of the circumference of a circle to its diameter
    DLMF defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2adec
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    base of natural logarithm
    DLMF defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2ahdec
    0 references
    imaginary unit
    DLMF defining formula
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2adec
    0 references
    complex variable
    DLMF defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C13.S1.XMD6.m1idec
    0 references

    Identifiers

     
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