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DLMF:9.12.E14 - MaRDI portal

DLMF:9.12.E14 (Q3640)

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DLMF:9.12.E14
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    Statements

    DLMF defining formula
    Hi ⁡ ( z ) = e ± 2 ⁢ π ⁢ i / 3 ⁢ Hi ⁡ ( z ⁢ e ± 2 ⁢ π ⁢ i / 3 ) + 2 ⁢ e ∓ π ⁢ i / 6 ⁢ Ai ⁡ ( z ⁢ e ∓ 2 ⁢ π ⁢ i / 3 ) . Scorer-Hi 𝑧 superscript 𝑒 plus-or-minus 2 𝜋 𝑖 3 Scorer-Hi 𝑧 superscript 𝑒 plus-or-minus 2 𝜋 𝑖 3 2 superscript 𝑒 minus-or-plus 𝜋 𝑖 6 Airy-Ai 𝑧 superscript 𝑒 minus-or-plus 2 𝜋 𝑖 3 {\displaystyle{\displaystyle\mathrm{Hi}\left(z\right)=e^{\pm 2\pi i/3}\mathrm{% Hi}\left(ze^{\pm 2\pi i/3}\right)+2e^{\mp\pi i/6}\mathrm{Ai}\left(ze^{\mp 2\pi i% /3}\right).}}
    0 references
    Symbols used
    Q10893
    DLMF defining formula
    Ai ⁡ ( z ) Airy-Ai 𝑧 {\displaystyle{\displaystyle\mathrm{Ai}\left(\NVar{z}\right)}}
    xml-id
    C9.S2.SS1.m1afdec
    0 references
    Scorer function (inhomogeneous Airy function)
    DLMF defining formula
    Hi ⁡ ( z ) Scorer-Hi 𝑧 {\displaystyle{\displaystyle\mathrm{Hi}\left(\NVar{z}\right)}}
    xml-id
    C9.S12.E5.m2ajdec
    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.m2agdec
    0 references
    base of natural logarithm
    DLMF defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2aedec
    0 references
    imaginary unit
    DLMF defining formula
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2aedec
    0 references
    complex variable
    DLMF defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C9.S1.XMD3.m1kdec
    0 references

    Identifiers

     
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