DLMF:31.10.E19 (Q9072): Difference between revisions

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‎Changed an Item: Add constraint
Property / Symbols used
 
Property / Symbols used: Q12499 / rank
 
Normal rank
Property / Symbols used: Q12499 / qualifier
 
Defining formula:

w 𝑤 {\displaystyle{\displaystyle w}}

w
Property / Symbols used: Q12499 / qualifier
 
xml-id: C31.S10.XMD16.m1edec

Revision as of 13:39, 2 January 2020

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DLMF:31.10.E19
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    Statements

    Defining formula
    𝒦 ⁢ ( u , v , w ) = u 1 - γ ⁢ v 1 - δ ⁢ w 1 - ϵ ⁢ 𝒞 1 - γ ⁡ ( u ⁢ σ 1 ) ⁢ 𝒞 1 - δ ⁡ ( v ⁢ σ 2 ) ⁢ 𝒞 1 - ϵ ⁡ ( i ⁢ w ⁢ σ 1 + σ 2 ) , 𝒦 𝑢 𝑣 𝑤 superscript 𝑢 1 𝛾 superscript 𝑣 1 𝛿 superscript 𝑤 1 italic-ϵ cylinder-function 1 𝛾 𝑢 subscript 𝜎 1 cylinder-function 1 𝛿 𝑣 subscript 𝜎 2 cylinder-function 1 italic-ϵ imaginary-unit 𝑤 subscript 𝜎 1 subscript 𝜎 2 {\displaystyle{\displaystyle\mathcal{K}(u,v,w)=u^{1-\gamma}v^{1-\delta}w^{1-% \epsilon}\mathscr{C}_{1-\gamma}\left(u\sqrt{\sigma_{1}}\right)\*\mathscr{C}_{1% -\delta}\left(v\sqrt{\sigma_{2}}\right)\mathscr{C}_{1-\epsilon}\left(\mathrm{i% }w\sqrt{\sigma_{1}+\sigma_{2}}\right),}}
    0 references
    DLMF id
    DLMF:31.10.E19
    0 references
    Symbols used
    Q11430
    Defining formula
    𝒞 ν ⁡ ( z ) cylinder-function 𝜈 𝑧 {\displaystyle{\displaystyle\mathscr{C}_{\NVar{\nu}}\left(\NVar{z}\right)}}
    xml-id
    C10.S2.Px5.p1.m3adec
    0 references
    imaginary unit
    Defining formula
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2abdec
    0 references
    Q12458
    Defining formula
    γ 𝛾 {\displaystyle{\displaystyle\gamma}}
    xml-id
    C31.S1.XMD10.m1idec
    0 references
    Q12459
    Defining formula
    δ 𝛿 {\displaystyle{\displaystyle\delta}}
    xml-id
    C31.S1.XMD11.m1idec
    0 references
    Q12460
    Defining formula
    ϵ italic-ϵ {\displaystyle{\displaystyle\epsilon}}
    xml-id
    C31.S1.XMD12.m1idec
    0 references
    kernel (locally)
    Defining formula
    𝒦 ⁢ ( z ; s , t ) 𝒦 𝑧 𝑠 𝑡 {\displaystyle{\displaystyle\mathcal{K}(z;s,t)}}
    xml-id
    C31.S10.XMD13.m1edec
    0 references
    Q12500
    Defining formula
    u 𝑢 {\displaystyle{\displaystyle u}}
    xml-id
    C31.S10.XMD14.m1bdec
    0 references
    Q12501
    Defining formula
    v 𝑣 {\displaystyle{\displaystyle v}}
    xml-id
    C31.S10.XMD15.m1bdec
    0 references
    Q12499
    Defining formula
    w 𝑤 {\displaystyle{\displaystyle w}}
    xml-id
    C31.S10.XMD16.m1edec
    0 references
     
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