DLMF:10.68.E12 (Q3879): 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: modulus of Bessel functions / rank
 
Normal rank
Property / Symbols used: modulus of Bessel functions / qualifier
 
Defining formula:

M ν ( x ) modulus-Bessel-M 𝜈 𝑥 {\displaystyle{\displaystyle M_{\NVar{\nu}}\left(\NVar{x}\right)}}

\HankelmodM{\NVar{\nu}}@{\NVar{x}}
Property / Symbols used: modulus of Bessel functions / qualifier
 
xml-id: C10.S18.E1.m2ahdec
Property / Symbols used
 
Property / Symbols used: Q11444 / rank
 
Normal rank
Property / Symbols used: Q11444 / qualifier
 
Defining formula:

θ ν ( x ) phase-Bessel-Theta 𝜈 𝑥 {\displaystyle{\displaystyle\theta_{\NVar{\nu}}\left(\NVar{x}\right)}}

\Hankelphasetheta{\NVar{\nu}}@{\NVar{x}}
Property / Symbols used: Q11444 / qualifier
 
xml-id: C10.S18.E3.m1ahdec
Property / Symbols used
 
Property / Symbols used: sine function / rank
 
Normal rank
Property / Symbols used: sine function / qualifier
 
Defining formula:

sin z 𝑧 {\displaystyle{\displaystyle\sin\NVar{z}}}

\sin@@{\NVar{z}}
Property / Symbols used: sine function / qualifier
 
xml-id: C4.S14.E1.m2addec
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.m1idec

Latest revision as of 14:30, 2 January 2020

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DLMF:10.68.E12
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    Statements

    θ ν = ( M ν + 1 / M ν ) sin ( θ ν + 1 - θ ν - 1 4 π ) = - ( M ν - 1 / M ν ) sin ( θ ν - 1 - θ ν - 1 4 π ) . diffop phase-Bessel-Theta 𝜈 1 modulus-Bessel-M 𝜈 1 modulus-Bessel-M 𝜈 phase-Bessel-Theta 𝜈 1 phase-Bessel-Theta 𝜈 1 4 𝜋 modulus-Bessel-M 𝜈 1 modulus-Bessel-M 𝜈 phase-Bessel-Theta 𝜈 1 phase-Bessel-Theta 𝜈 1 4 𝜋 {\displaystyle{\displaystyle\theta_{\nu}'=(M_{\nu+1}/M_{\nu})\sin\left(\theta_% {\nu+1}-\theta_{\nu}-\tfrac{1}{4}\pi\right)=-(M_{\nu-1}/M_{\nu})\sin\left(% \theta_{\nu-1}-\theta_{\nu}-\tfrac{1}{4}\pi\right).}}
    0 references
    DLMF:10.68.E12
    0 references
    π {\displaystyle{\displaystyle\pi}}
    C3.S12.E1.m2aedec
    0 references
    M ν ( x ) modulus-Bessel-M 𝜈 𝑥 {\displaystyle{\displaystyle M_{\NVar{\nu}}\left(\NVar{x}\right)}}
    C10.S18.E1.m2ahdec
    0 references
    θ ν ( x ) phase-Bessel-Theta 𝜈 𝑥 {\displaystyle{\displaystyle\theta_{\NVar{\nu}}\left(\NVar{x}\right)}}
    C10.S18.E3.m1ahdec
    0 references
    sin z 𝑧 {\displaystyle{\displaystyle\sin\NVar{z}}}
    C4.S14.E1.m2addec
    0 references
    ν 𝜈 {\displaystyle{\displaystyle\nu}}
    C10.S1.XMD7.m1idec
    0 references