DLMF:10.68.E2 (Q3863): Difference between revisions

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Changed an Item: Add constraint
Changed an Item: Add constraint
 
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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.m2aadec
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.m2aadec
Property / Symbols used
 
Property / Symbols used: modulus of derivatives of Bessel functions / rank
 
Normal rank
Property / Symbols used: modulus of derivatives of Bessel functions / qualifier
 
Defining formula:

N ν ( x ) modulus-Bessel-N 𝜈 𝑥 {\displaystyle{\displaystyle N_{\NVar{\nu}}\left(\NVar{x}\right)}}

\HankelmodderivN{\NVar{\nu}}@{\NVar{x}}
Property / Symbols used: modulus of derivatives of Bessel functions / qualifier
 
xml-id: C10.S18.E2.m2adec
Property / Symbols used
 
Property / Symbols used: Q11445 / rank
 
Normal rank
Property / Symbols used: Q11445 / qualifier
 
Defining formula:

ϕ ν ( x ) phase-Bessel-Phi 𝜈 𝑥 {\displaystyle{\displaystyle\phi_{\NVar{\nu}}\left(\NVar{x}\right)}}

\Hankelphasederivphi{\NVar{\nu}}@{\NVar{x}}
Property / Symbols used: Q11445 / qualifier
 
xml-id: C10.S18.E3.m2adec
Property / Symbols used
 
Property / Symbols used: Q11435 / rank
 
Normal rank
Property / Symbols used: Q11435 / qualifier
 
Defining formula:

x 𝑥 {\displaystyle{\displaystyle x}}

x
Property / Symbols used: Q11435 / qualifier
 
xml-id: C10.S1.XMD4.m1adec
Property / Symbols used
 
Property / Symbols used: Q11427 / rank
 
Normal rank
Property / Symbols used: Q11427 / qualifier
 
Defining formula:

ν 𝜈 {\displaystyle{\displaystyle\nu}}

\nu
Property / Symbols used: Q11427 / qualifier
 
xml-id: C10.S1.XMD7.m1adec

Latest revision as of 14:29, 2 January 2020

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DLMF:10.68.E2
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    Statements

    N ν ( x ) e i ϕ ν ( x ) = ker ν x + i kei ν x , modulus-Bessel-N 𝜈 𝑥 superscript 𝑒 𝑖 phase-Bessel-Phi 𝜈 𝑥 Kelvin-ker 𝜈 𝑥 𝑖 Kelvin-kei 𝜈 𝑥 {\displaystyle{\displaystyle N_{\nu}\left(x\right)e^{i\phi_{\nu}\left(x\right)% }=\operatorname{ker}_{\nu}x+i\operatorname{kei}_{\nu}x,}}
    0 references
    DLMF:10.68.E2
    0 references
    kei ν ( x ) Kelvin-kei 𝜈 𝑥 {\displaystyle{\displaystyle\operatorname{kei}_{\NVar{\nu}}\left(\NVar{x}% \right)}}
    C10.S61.E2.m3adec
    0 references
    ker ν ( x ) Kelvin-ker 𝜈 𝑥 {\displaystyle{\displaystyle\operatorname{ker}_{\NVar{\nu}}\left(\NVar{x}% \right)}}
    C10.S61.E2.m2adec
    0 references
    e {\displaystyle{\displaystyle\mathrm{e}}}
    C4.S2.E11.m2aadec
    0 references
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    C1.S9.E1.m2aadec
    0 references
    N ν ( x ) modulus-Bessel-N 𝜈 𝑥 {\displaystyle{\displaystyle N_{\NVar{\nu}}\left(\NVar{x}\right)}}
    C10.S18.E2.m2adec
    0 references
    ϕ ν ( x ) phase-Bessel-Phi 𝜈 𝑥 {\displaystyle{\displaystyle\phi_{\NVar{\nu}}\left(\NVar{x}\right)}}
    C10.S18.E3.m2adec
    0 references
    x 𝑥 {\displaystyle{\displaystyle x}}
    C10.S1.XMD4.m1adec
    0 references
    ν 𝜈 {\displaystyle{\displaystyle\nu}}
    C10.S1.XMD7.m1adec
    0 references