DLMF:10.18.E1 (Q3188): Difference between revisions

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‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
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.m2adec

Revision as of 15:33, 2 January 2020

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DLMF:10.18.E1
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    Statements

    Defining formula
    M ν ⁡ ( x ) ⁢ e i ⁢ θ ν ⁡ ( x ) = H ν ( 1 ) ⁡ ( x ) , modulus-Bessel-M 𝜈 𝑥 superscript 𝑒 𝑖 phase-Bessel-Theta 𝜈 𝑥 Hankel-H-1-Bessel-third-kind 𝜈 𝑥 {\displaystyle{\displaystyle M_{\nu}\left(x\right)e^{i\theta_{\nu}\left(x% \right)}={H^{(1)}_{\nu}}\left(x\right),}}
    0 references
    DLMF id
    DLMF:10.18.E1
    0 references
    Symbols used
    Bessel function of the third kind (or Hankel function)
    Defining formula
    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.m2adec
    0 references
    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2adec
    0 references
    imaginary unit
    Defining formula
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2adec
    0 references
     
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