DLMF:9.11.E19 (Q2926): Difference between revisions

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‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
Property / Symbols used
 
Property / Symbols used: the ratio of the circumference of a circle to its diameter / rank
 
Normal rank
Property / Symbols used: the ratio of the circumference of a circle to its diameter / qualifier
 
Defining formula:

π {\displaystyle{\displaystyle\pi}}

\cpi
Property / Symbols used: the ratio of the circumference of a circle to its diameter / qualifier
 
xml-id: C3.S12.E1.m2ajdec

Revision as of 14:51, 2 January 2020

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DLMF:9.11.E19
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    Statements

    Defining formula
    ∫ 0 ∞ d t Ai 2 ⁡ ( t ) + Bi 2 ⁡ ( t ) = ∫ 0 ∞ t ⁢ d t Ai ′ 2 ⁡ ( t ) + Bi ′ 2 ⁡ ( t ) = π 2 6 . superscript subscript 0 𝑡 Airy-Ai 2 𝑡 Airy-Bi 2 𝑡 superscript subscript 0 𝑡 𝑡 diffop Airy-Ai 1 2 𝑡 diffop Airy-Bi 1 2 𝑡 superscript 𝜋 2 6 {\displaystyle{\displaystyle\int_{0}^{\infty}\frac{\mathrm{d}t}{{\mathrm{Ai}^{% 2}}\left(t\right)+{\mathrm{Bi}^{2}}\left(t\right)}=\int_{0}^{\infty}\frac{t% \mathrm{d}t}{{\mathrm{Ai}'^{2}}\left(t\right)+{\mathrm{Bi}'^{2}}\left(t\right)% }=\frac{\pi^{2}}{6}.}}
    0 references
    DLMF id
    DLMF:9.11.E19
    0 references
    Symbols used
    Q10919
    Defining formula
    Ai ⁡ ( z ) Airy-Ai 𝑧 {\displaystyle{\displaystyle\mathrm{Ai}\left(\NVar{z}\right)}}
    xml-id
    C9.S2.SS1.m1ajdec
    0 references
    Q11081
    Defining formula
    Bi ⁡ ( z ) Airy-Bi 𝑧 {\displaystyle{\displaystyle\mathrm{Bi}\left(\NVar{z}\right)}}
    xml-id
    C9.S2.SS1.m2afdec
    0 references
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2ajdec
    0 references
     
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