DLMF:10.61.E1 (Q3790): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Bessel function of the first kind / rank
 
Normal rank
Property / Symbols used: Bessel function of the first kind / qualifier
 
test:

J ν ⁡ ( z ) Bessel-J 𝜈 𝑧 {\displaystyle{\displaystyle J_{\NVar{\nu}}\left(\NVar{z}\right)}}

\BesselJ{\NVar{\nu}}@{\NVar{z}}
Property / Symbols used: Bessel function of the first kind / qualifier
 
xml-id: C10.S2.E2.m2adec
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.m2adec
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.m2adec
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.m2adec
Property / Symbols used
 
Property / Symbols used: modified Bessel function of the first kind / rank
 
Normal rank
Property / Symbols used: modified Bessel function of the first kind / qualifier
 
test:

I ν ⁡ ( z ) modified-Bessel-first-kind 𝜈 𝑧 {\displaystyle{\displaystyle I_{\NVar{\nu}}\left(\NVar{z}\right)}}

\modBesselI{\NVar{\nu}}@{\NVar{z}}
Property / Symbols used: modified Bessel function of the first kind / qualifier
 
xml-id: C10.S25.E2.m2adec
Property / Symbols used
 
Property / Symbols used: Q11435 / rank
 
Normal rank
Property / Symbols used: Q11435 / qualifier
 
test:

x 𝑥 {\displaystyle{\displaystyle x}}

x
Property / Symbols used: Q11435 / qualifier
 
xml-id: C10.S1.XMD4.m1dec
Property / Symbols used
 
Property / Symbols used: Q11427 / rank
 
Normal rank
Property / Symbols used: Q11427 / qualifier
 
test:

ν 𝜈 {\displaystyle{\displaystyle\nu}}

\nu
Property / Symbols used: Q11427 / qualifier
 
xml-id: C10.S1.XMD7.m1dec

Latest revision as of 13:20, 2 January 2020

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DLMF:10.61.E1
No description defined

    Statements

    test
    ber ν ⁡ x + i ⁢ bei ν ⁡ x = J ν ⁡ ( x ⁢ e 3 ⁢ π ⁢ i / 4 ) = e ν ⁢ π ⁢ i ⁢ J ν ⁡ ( x ⁢ e - π ⁢ i / 4 ) = e ν ⁢ π ⁢ i / 2 ⁢ I ν ⁡ ( x ⁢ e π ⁢ i / 4 ) = e 3 ⁢ ν ⁢ π ⁢ i / 2 ⁢ I ν ⁡ ( x ⁢ e - 3 ⁢ π ⁢ i / 4 ) , Kelvin-ber 𝜈 𝑥 𝑖 Kelvin-bei 𝜈 𝑥 Bessel-J 𝜈 𝑥 superscript 𝑒 3 𝜋 𝑖 4 superscript 𝑒 𝜈 𝜋 𝑖 Bessel-J 𝜈 𝑥 superscript 𝑒 𝜋 𝑖 4 superscript 𝑒 𝜈 𝜋 𝑖 2 modified-Bessel-first-kind 𝜈 𝑥 superscript 𝑒 𝜋 𝑖 4 superscript 𝑒 3 𝜈 𝜋 𝑖 2 modified-Bessel-first-kind 𝜈 𝑥 superscript 𝑒 3 𝜋 𝑖 4 {\displaystyle{\displaystyle\operatorname{ber}_{\nu}x+i\operatorname{bei}_{\nu% }x=J_{\nu}\left(xe^{3\pi i/4}\right)=e^{\nu\pi i}J_{\nu}\left(xe^{-\pi i/4}% \right)=e^{\nu\pi i/2}I_{\nu}\left(xe^{\pi i/4}\right)=e^{3\nu\pi i/2}I_{\nu}% \left(xe^{-3\pi i/4}\right),}}
    0 references
    DLMF id
    DLMF:10.61.E1
    0 references
    Symbols defined
    Kelvin function
    0 references
    Kelvin function
    0 references
    Symbols used
    Bessel function of the first kind
    test
    J ν ⁡ ( z ) Bessel-J 𝜈 𝑧 {\displaystyle{\displaystyle J_{\NVar{\nu}}\left(\NVar{z}\right)}}
    xml-id
    C10.S2.E2.m2adec
    0 references
    the ratio of the circumference of a circle to its diameter
    test
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2adec
    0 references
    base of natural logarithm
    test
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2adec
    0 references
    imaginary unit
    test
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2adec
    0 references
    modified Bessel function of the first kind
    test
    I ν ⁡ ( z ) modified-Bessel-first-kind 𝜈 𝑧 {\displaystyle{\displaystyle I_{\NVar{\nu}}\left(\NVar{z}\right)}}
    xml-id
    C10.S25.E2.m2adec
    0 references
    Q11435
    test
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C10.S1.XMD4.m1dec
    0 references
    Q11427
    test
    ν 𝜈 {\displaystyle{\displaystyle\nu}}
    xml-id
    C10.S1.XMD7.m1dec
    0 references
     
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