Deprecated: $wgMWOAuthSharedUserIDs=false is deprecated, set $wgMWOAuthSharedUserIDs=true, $wgMWOAuthSharedUserSource='local' instead [Called from MediaWiki\HookContainer\HookContainer::run in /var/www/html/w/includes/HookContainer/HookContainer.php at line 135] in /var/www/html/w/includes/Debug/MWDebug.php on line 372
DLMF:10.68.E12 - MaRDI portal

DLMF:10.68.E12 (Q4576)

From MaRDI portal





No description defined
Language Label Description Also known as
English
DLMF:10.68.E12
No description defined

    Statements

    DLMF defining formula
    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
    Symbols used
    the ratio of the circumference of a circle to its diameter
    DLMF defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2aedec
    0 references
    modulus of Bessel functions
    DLMF defining formula
    M ν ⁡ ( x ) modulus-Bessel-M 𝜈 𝑥 {\displaystyle{\displaystyle M_{\NVar{\nu}}\left(\NVar{x}\right)}}
    xml-id
    C10.S18.E1.m2ahdec
    0 references
    phase of Bessel functions
    DLMF defining formula
    θ ν ⁡ ( x ) phase-Bessel-Theta 𝜈 𝑥 {\displaystyle{\displaystyle\theta_{\NVar{\nu}}\left(\NVar{x}\right)}}
    xml-id
    C10.S18.E3.m1ahdec
    0 references
    sine function
    DLMF defining formula
    sin ⁡ z 𝑧 {\displaystyle{\displaystyle\sin\NVar{z}}}
    xml-id
    C4.S14.E1.m2addec
    0 references
    complex parameter
    DLMF defining formula
    ν 𝜈 {\displaystyle{\displaystyle\nu}}
    xml-id
    C10.S1.XMD7.m1idec
    0 references

    Identifiers

     
    Retrieved from "https://portal.mardi4nfdi.de/w/index.php?title=Item:Q4576&oldid=24171924"
    Powered by MediaWiki