DLMF:9.6.E16 (Q2796): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q10919 / rank
 
Normal rank
Property / Symbols used: Q10919 / qualifier
 
test:

Ai ( z ) Airy-Ai 𝑧 {\displaystyle{\displaystyle\mathrm{Ai}\left(\NVar{z}\right)}}

\AiryAi@{\NVar{z}}
Property / Symbols used: Q10919 / qualifier
 
xml-id: C9.S2.SS1.m1aidec
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
 
test:

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.m2aidec
Property / Symbols used
 
Property / Symbols used: modified Bessel function of the second kind / rank
 
Normal rank
Property / Symbols used: modified Bessel function of the second kind / qualifier
 
test:

K ν ( z ) modified-Bessel-second-kind 𝜈 𝑧 {\displaystyle{\displaystyle K_{\NVar{\nu}}\left(\NVar{z}\right)}}

\modBesselK{\NVar{\nu}}@{\NVar{z}}
Property / Symbols used: modified Bessel function of the second kind / qualifier
 
xml-id: C10.S25.E3.m2acdec
Property / Symbols used
 
Property / Symbols used: Q11381 / rank
 
Normal rank
Property / Symbols used: Q11381 / qualifier
 
test:

z 𝑧 {\displaystyle{\displaystyle z}}

z
Property / Symbols used: Q11381 / qualifier
 
xml-id: C9.S1.XMD3.m1odec
Property / Symbols used
 
Property / Symbols used: change of variable (locally) / rank
 
Normal rank
Property / Symbols used: change of variable (locally) / qualifier
 
test:

ζ ( z ) 𝜁 𝑧 {\displaystyle{\displaystyle\zeta(z)}}

\zeta(z)
Property / Symbols used: change of variable (locally) / qualifier
 
xml-id: C9.S6.XMD2.m1fdec

Latest revision as of 14:29, 2 January 2020

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DLMF:9.6.E16
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    Statements

    K ± 2 / 3 ( ζ ) = - π ( 3 / z ) Ai ( z ) , modified-Bessel-second-kind plus-or-minus 2 3 𝜁 𝜋 3 𝑧 diffop Airy-Ai 1 𝑧 {\displaystyle{\displaystyle K_{\pm 2/3}\left(\zeta\right)=-\pi(\sqrt{3}/z)% \mathrm{Ai}'\left(z\right),}}
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    Ai ( z ) Airy-Ai 𝑧 {\displaystyle{\displaystyle\mathrm{Ai}\left(\NVar{z}\right)}}
    C9.S2.SS1.m1aidec
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    π {\displaystyle{\displaystyle\pi}}
    C3.S12.E1.m2aidec
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    K ν ( z ) modified-Bessel-second-kind 𝜈 𝑧 {\displaystyle{\displaystyle K_{\NVar{\nu}}\left(\NVar{z}\right)}}
    C10.S25.E3.m2acdec
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    z 𝑧 {\displaystyle{\displaystyle z}}
    C9.S1.XMD3.m1odec
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    ζ ( z ) 𝜁 𝑧 {\displaystyle{\displaystyle\zeta(z)}}
    C9.S6.XMD2.m1fdec
    0 references