DLMF:9.6.E17 (Q2797): Difference between revisions

From testwiki
Jump to navigation Jump to search
imported>Admin
 
imported>Admin
 
(6 intermediate revisions by the same user not shown)
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.m1ajdec
Property / Symbols used
 
Property / Symbols used: Q11081 / rank
 
Normal rank
Property / Symbols used: Q11081 / qualifier
 
test:

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

\AiryBi@{\NVar{z}}
Property / Symbols used: Q11081 / qualifier
 
xml-id: C9.S2.SS1.m2ahdec
Property / Symbols used
 
Property / Symbols used: Bessel function of the third kind (or Hankel function) / rank
 
Normal rank
Property / Symbols used: Bessel function of the third kind (or Hankel function) / qualifier
 
test:

H ν ( 1 ) ⁡ ( z ) Hankel-H-1-Bessel-third-kind 𝜈 𝑧 {\displaystyle{\displaystyle{H^{(1)}_{\NVar{\nu}}}\left(\NVar{z}\right)}}

\HankelH{1}{\NVar{\nu}}@{\NVar{z}}
Property / Symbols used: Bessel function of the third kind (or Hankel function) / qualifier
 
xml-id: C10.S2.E5.m2ahdec
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.m2ajdec
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.m2ahdec
Property / Symbols used
 
Property / Symbols used: imaginary unit / rank
 
Normal rank
Property / Symbols used: imaginary unit / qualifier
 
test:

i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}

\iunit
Property / Symbols used: imaginary unit / qualifier
 
xml-id: C1.S9.E1.m2ahdec
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.m1pdec

Latest revision as of 13:29, 2 January 2020

No description defined
Language Label Description Also known as
English
DLMF:9.6.E17
No description defined

    Statements

    test
    H 1 / 3 ( 1 ) ⁡ ( ζ ) = e - π ⁢ i / 3 ⁢ H - 1 / 3 ( 1 ) ⁡ ( ζ ) = e - π ⁢ i / 6 ⁢ 3 / z ⁢ ( Ai ⁡ ( - z ) - i ⁢ Bi ⁡ ( - z ) ) , Hankel-H-1-Bessel-third-kind 1 3 𝜁 superscript 𝑒 𝜋 𝑖 3 Hankel-H-1-Bessel-third-kind 1 3 𝜁 superscript 𝑒 𝜋 𝑖 6 3 𝑧 Airy-Ai 𝑧 𝑖 Airy-Bi 𝑧 {\displaystyle{\displaystyle{H^{(1)}_{1/3}}\left(\zeta\right)=e^{-\pi i/3}{H^{% (1)}_{-1/3}}\left(\zeta\right)=e^{-\pi i/6}\sqrt{3/z}\left(\mathrm{Ai}\left(-z% \right)-i\mathrm{Bi}\left(-z\right)\right),}}
    0 references
    DLMF id
    DLMF:9.6.E17
    0 references
    Symbols used
    Q10919
    test
    Ai ⁡ ( z ) Airy-Ai 𝑧 {\displaystyle{\displaystyle\mathrm{Ai}\left(\NVar{z}\right)}}
    xml-id
    C9.S2.SS1.m1ajdec
    0 references
    Q11081
    test
    Bi ⁡ ( z ) Airy-Bi 𝑧 {\displaystyle{\displaystyle\mathrm{Bi}\left(\NVar{z}\right)}}
    xml-id
    C9.S2.SS1.m2ahdec
    0 references
    Bessel function of the third kind (or Hankel function)
    test
    H ν ( 1 ) ⁡ ( z ) Hankel-H-1-Bessel-third-kind 𝜈 𝑧 {\displaystyle{\displaystyle{H^{(1)}_{\NVar{\nu}}}\left(\NVar{z}\right)}}
    xml-id
    C10.S2.E5.m2ahdec
    0 references
    the ratio of the circumference of a circle to its diameter
    test
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2ajdec
    0 references
    base of natural logarithm
    test
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2ahdec
    0 references
    imaginary unit
    test
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2ahdec
    0 references
    Q11381
    test
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C9.S1.XMD3.m1pdec
    0 references
     
      Retrieved from "https://lct.wmflabs.org/w/index.php?title=Item:Q2797&oldid=14405"