DLMF:9.6.E19 (Q2799): Difference between revisions

From DRMF
Jump to navigation Jump to search
Changed an Item: Add constraint
Changed an Item: Add constraint
 
(6 intermediate revisions by the same user not shown)
Property / Symbols used
 
Property / Symbols used: Q11081 / rank
 
Normal rank
Property / Symbols used: Q11081 / qualifier
 
Defining formula:

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.m2ajdec
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
 
Defining formula:

H ν ( 2 ) ( z ) Hankel-H-2-Bessel-third-kind 𝜈 𝑧 {\displaystyle{\displaystyle{H^{(2)}_{\NVar{\nu}}}\left(\NVar{z}\right)}}

\HankelH{2}{\NVar{\nu}}@{\NVar{z}}
Property / Symbols used: Bessel function of the third kind (or Hankel function) / qualifier
 
xml-id: C10.S2.E6.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
 
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.m2aldec
Property / Symbols used
 
Property / Symbols used: base of natural logarithm / rank
 
Normal rank
Property / Symbols used: base of natural logarithm / qualifier
 
Defining formula:

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

\expe
Property / Symbols used: base of natural logarithm / qualifier
 
xml-id: C4.S2.E11.m2ajdec
Property / Symbols used
 
Property / Symbols used: imaginary unit / rank
 
Normal rank
Property / Symbols used: imaginary unit / qualifier
 
Defining formula:

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

\iunit
Property / Symbols used: imaginary unit / qualifier
 
xml-id: C1.S9.E1.m2ajdec
Property / Symbols used
 
Property / Symbols used: Q11381 / rank
 
Normal rank
Property / Symbols used: Q11381 / qualifier
 
Defining formula:

z 𝑧 {\displaystyle{\displaystyle z}}

z
Property / Symbols used: Q11381 / qualifier
 
xml-id: C9.S1.XMD3.m1rdec
Property / Symbols used
 
Property / Symbols used: change of variable (locally) / rank
 
Normal rank
Property / Symbols used: change of variable (locally) / qualifier
 
Defining formula:

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

\zeta(z)
Property / Symbols used: change of variable (locally) / qualifier
 
xml-id: C9.S6.XMD2.m1idec

Latest revision as of 14:30, 2 January 2020

No description defined
Language Label Description Also known as
English
DLMF:9.6.E19
No description defined

    Statements

    H 1 / 3 ( 2 ) ( ζ ) = e π i / 3 H - 1 / 3 ( 2 ) ( ζ ) = e π i / 6 3 / z ( Ai ( - z ) + i Bi ( - z ) ) , Hankel-H-2-Bessel-third-kind 1 3 𝜁 superscript 𝑒 𝜋 𝑖 3 Hankel-H-2-Bessel-third-kind 1 3 𝜁 superscript 𝑒 𝜋 𝑖 6 3 𝑧 Airy-Ai 𝑧 𝑖 Airy-Bi 𝑧 {\displaystyle{\displaystyle{H^{(2)}_{1/3}}\left(\zeta\right)=e^{\pi i/3}{H^{(% 2)}_{-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:9.6.E19
    0 references
    Ai ( z ) Airy-Ai 𝑧 {\displaystyle{\displaystyle\mathrm{Ai}\left(\NVar{z}\right)}}
    C9.S2.SS1.m1aldec
    0 references
    Bi ( z ) Airy-Bi 𝑧 {\displaystyle{\displaystyle\mathrm{Bi}\left(\NVar{z}\right)}}
    C9.S2.SS1.m2ajdec
    0 references
    H ν ( 2 ) ( z ) Hankel-H-2-Bessel-third-kind 𝜈 𝑧 {\displaystyle{\displaystyle{H^{(2)}_{\NVar{\nu}}}\left(\NVar{z}\right)}}
    C10.S2.E6.m2ahdec
    0 references
    π {\displaystyle{\displaystyle\pi}}
    C3.S12.E1.m2aldec
    0 references
    e {\displaystyle{\displaystyle\mathrm{e}}}
    C4.S2.E11.m2ajdec
    0 references
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    C1.S9.E1.m2ajdec
    0 references
    z 𝑧 {\displaystyle{\displaystyle z}}
    C9.S1.XMD3.m1rdec
    0 references
    ζ ( z ) 𝜁 𝑧 {\displaystyle{\displaystyle\zeta(z)}}
    C9.S6.XMD2.m1idec
    0 references