DLMF:9.12.E10 (Q2938): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: base of natural logarithm / rank
 
Normal rank
Property / Symbols used: base of natural logarithm / qualifier
 
test:

e {\displaystyle{\displaystyle\mathrm{e}}}

\expe
Property / Symbols used: base of natural logarithm / qualifier
 
xml-id: C4.S2.E11.m2abdec

Revision as of 13:53, 2 January 2020

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DLMF:9.12.E10
No description defined

    Statements

    test
    e ∓ 2 ⁢ π ⁢ i / 3 ⁢ Hi ⁡ ( z ⁢ e ∓ 2 ⁢ π ⁢ i / 3 ) , Ai ⁡ ( z ) , Ai ⁡ ( z ⁢ e ± 2 ⁢ π ⁢ i / 3 ) , superscript 𝑒 minus-or-plus 2 𝜋 𝑖 3 Scorer-Hi 𝑧 superscript 𝑒 minus-or-plus 2 𝜋 𝑖 3 Airy-Ai 𝑧 Airy-Ai 𝑧 superscript 𝑒 plus-or-minus 2 𝜋 𝑖 3 {\displaystyle{\displaystyle e^{\mp 2\pi i/3}\mathrm{Hi}\left(ze^{\mp 2\pi i/3% }\right),\mathrm{Ai}\left(z\right),\mathrm{Ai}\left(ze^{\pm 2\pi i/3}\right),}}
    0 references
    DLMF id
    DLMF:9.12.E10
    0 references
    constraint
    - π ≤ ± ph ⁡ z ≤ 1 3 ⁢ π 𝜋 plus-or-minus phase 𝑧 1 3 𝜋 {\displaystyle{\displaystyle-\pi\leq\pm\operatorname{ph}z\leq\tfrac{1}{3}\pi}}
    0 references
    Symbols used
    Q10919
    test
    Ai ⁡ ( z ) Airy-Ai 𝑧 {\displaystyle{\displaystyle\mathrm{Ai}\left(\NVar{z}\right)}}
    xml-id
    C9.S2.SS1.m1addec
    0 references
    Scorer function (inhomogeneous Airy function)
    test
    Hi ⁡ ( z ) Scorer-Hi 𝑧 {\displaystyle{\displaystyle\mathrm{Hi}\left(\NVar{z}\right)}}
    xml-id
    C9.S12.E5.m2afdec
    0 references
    the ratio of the circumference of a circle to its diameter
    test
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2addec
    0 references
    base of natural logarithm
    test
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2abdec
    0 references
     
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