DLMF:2.8.E34 (Q970): 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.m2acdec
Property / Symbols used
 
Property / Symbols used: Bessel function of the second kind / rank
 
Normal rank
Property / Symbols used: Bessel function of the second kind / qualifier
 
test:

Y ν ⁡ ( z ) Bessel-Y-Weber 𝜈 𝑧 {\displaystyle{\displaystyle Y_{\NVar{\nu}}\left(\NVar{z}\right)}}

\BesselY{\NVar{\nu}}@{\NVar{z}}
Property / Symbols used: Bessel function of the second kind / qualifier
 
xml-id: C10.S2.E3.m2acdec
Property / Symbols used
 
Property / Symbols used: Q11090 / rank
 
Normal rank
Property / Symbols used: Q11090 / qualifier
 
test:

env ⁢ J ν ⁡ ( x ) envelope-Bessel-J 𝜈 𝑥 {\displaystyle{\displaystyle\mathrm{env}\mskip-2.0mu J_{\NVar{\nu}}\left(\NVar% {x}\right)}}

\envBesselJ{\NVar{\nu}}@{\NVar{x}}
Property / Symbols used: Q11090 / qualifier
 
xml-id: C2.S8.SS4.p5.m2aadec
Property / Symbols used
 
Property / Symbols used: Q11091 / rank
 
Normal rank
Property / Symbols used: Q11091 / qualifier
 
test:

env ⁢ Y ν ⁡ ( x ) envelope-Bessel-Y 𝜈 𝑥 {\displaystyle{\displaystyle\mathrm{env}\mskip-2.0mu Y_{\NVar{\nu}}\left(\NVar% {x}\right)}}

\envBesselY{\NVar{\nu}}@{\NVar{x}}
Property / Symbols used: Q11091 / qualifier
 
xml-id: C2.S8.SS4.p5.m4aadec
Property / Symbols used
 
Property / Symbols used: Q11086 / rank
 
Normal rank
Property / Symbols used: Q11086 / qualifier
 
test:

ν 𝜈 {\displaystyle{\displaystyle\nu}}

\nu
Property / Symbols used: Q11086 / qualifier
 
xml-id: C2.S8.XMD21.m1jdec
Property / Symbols used
 
Property / Symbols used: Q11092 / rank
 
Normal rank
Property / Symbols used: Q11092 / qualifier
 
test:

X ν subscript 𝑋 𝜈 {\displaystyle{\displaystyle X_{\nu}}}

X_{\nu}
Property / Symbols used: Q11092 / qualifier
 
xml-id: C2.S8.XMD25.m1adec

Latest revision as of 16:30, 1 January 2020

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DLMF:2.8.E34
No description defined

    Statements

    test
    env ⁢ J ν ⁡ ( x ) = env ⁢ Y ν ⁡ ( x ) = ( J ν 2 ⁢ ( x ) + Y ν 2 ⁢ ( x ) ) 1 / 2 , envelope-Bessel-J 𝜈 𝑥 envelope-Bessel-Y 𝜈 𝑥 superscript Bessel-J 𝜈 2 𝑥 Bessel-Y-Weber 𝜈 2 𝑥 1 2 {\displaystyle{\displaystyle\mathrm{env}\mskip-2.0mu J_{\nu}(x)=\mathrm{env}% \mskip-2.0mu Y_{\nu}(x)=\left({J_{\nu}^{2}}(x)+{Y_{\nu}^{2}}(x)\right)^{1/2},}}
    0 references
    DLMF id
    DLMF:2.8.E34
    0 references
    constraint
    X ν ≤ x < ∞ subscript 𝑋 𝜈 𝑥 {\displaystyle{\displaystyle X_{\nu}\leq x<\infty}}
    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.m2acdec
    0 references
    Bessel function of the second kind
    test
    Y ν ⁡ ( z ) Bessel-Y-Weber 𝜈 𝑧 {\displaystyle{\displaystyle Y_{\NVar{\nu}}\left(\NVar{z}\right)}}
    xml-id
    C10.S2.E3.m2acdec
    0 references
    Q11090
    test
    env ⁢ J ν ⁡ ( x ) envelope-Bessel-J 𝜈 𝑥 {\displaystyle{\displaystyle\mathrm{env}\mskip-2.0mu J_{\NVar{\nu}}\left(\NVar% {x}\right)}}
    xml-id
    C2.S8.SS4.p5.m2aadec
    0 references
    Q11091
    test
    env ⁢ Y ν ⁡ ( x ) envelope-Bessel-Y 𝜈 𝑥 {\displaystyle{\displaystyle\mathrm{env}\mskip-2.0mu Y_{\NVar{\nu}}\left(\NVar% {x}\right)}}
    xml-id
    C2.S8.SS4.p5.m4aadec
    0 references
    Q11086
    test
    ν 𝜈 {\displaystyle{\displaystyle\nu}}
    xml-id
    C2.S8.XMD21.m1jdec
    0 references
    Q11092
    test
    X ν subscript 𝑋 𝜈 {\displaystyle{\displaystyle X_{\nu}}}
    xml-id
    C2.S8.XMD25.m1adec
    0 references
     
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