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DLMF:22.9.E22 - MaRDI portal

DLMF:22.9.E22 (Q7707)

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DLMF:22.9.E22
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    Statements

    DLMF defining formula
    s 1 , 3 ( 2 ) ⁢ c 1 , 3 ( 2 ) ⁢ d 2 , 3 ( 2 ) ⁢ d 3 , 3 ( 2 ) + s 2 , 3 ( 2 ) ⁢ c 2 , 3 ( 2 ) ⁢ d 3 , 3 ( 2 ) ⁢ d 1 , 3 ( 2 ) + s 3 , 3 ( 2 ) ⁢ c 3 , 3 ( 2 ) ⁢ d 1 , 3 ( 2 ) ⁢ d 2 , 3 ( 2 ) = κ 2 + k 2 - 1 1 - κ 2 ⁢ ( s 1 , 3 ( 2 ) ⁢ c 1 , 3 ( 2 ) + s 2 , 3 ( 2 ) ⁢ c 2 , 3 ( 2 ) + s 3 , 3 ( 2 ) ⁢ c 3 , 3 ( 2 ) ) , superscript subscript 𝑠 1 3 2 superscript subscript 𝑐 1 3 2 superscript subscript 𝑑 2 3 2 superscript subscript 𝑑 3 3 2 superscript subscript 𝑠 2 3 2 superscript subscript 𝑐 2 3 2 superscript subscript 𝑑 3 3 2 superscript subscript 𝑑 1 3 2 superscript subscript 𝑠 3 3 2 superscript subscript 𝑐 3 3 2 superscript subscript 𝑑 1 3 2 superscript subscript 𝑑 2 3 2 superscript 𝜅 2 superscript 𝑘 2 1 1 superscript 𝜅 2 superscript subscript 𝑠 1 3 2 superscript subscript 𝑐 1 3 2 superscript subscript 𝑠 2 3 2 superscript subscript 𝑐 2 3 2 superscript subscript 𝑠 3 3 2 superscript subscript 𝑐 3 3 2 {\displaystyle{\displaystyle s_{1,3}^{(2)}c_{1,3}^{(2)}d_{2,3}^{(2)}d_{3,3}^{(% 2)}+s_{2,3}^{(2)}c_{2,3}^{(2)}d_{3,3}^{(2)}d_{1,3}^{(2)}+s_{3,3}^{(2)}c_{3,3}^% {(2)}d_{1,3}^{(2)}d_{2,3}^{(2)}=\frac{\kappa^{2}+k^{2}-1}{1-\kappa^{2}}\left(s% _{1,3}^{(2)}c_{1,3}^{(2)}+s_{2,3}^{(2)}c_{2,3}^{(2)}+s_{3,3}^{(2)}c_{3,3}^{(2)% }\right),}}
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    comment
    Warning: Falling back to standard tex;
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    Symbols used
    modulus
    DLMF defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C22.S1.XMD4.m1jdec
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    cyclic quantity
    DLMF defining formula
    s m , p ( r ) superscript subscript 𝑠 𝑚 𝑝 𝑟 {\displaystyle{\displaystyle s_{m,p}^{(r)}}}
    xml-id
    C22.S9.XMD3.m1hdec
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    cyclic quantity
    DLMF defining formula
    c m , p ( r ) superscript subscript 𝑐 𝑚 𝑝 𝑟 {\displaystyle{\displaystyle c_{m,p}^{(r)}}}
    xml-id
    C22.S9.XMD4.m1hdec
    0 references
    cyclic quantity
    DLMF defining formula
    d m , p ( r ) superscript subscript 𝑑 𝑚 𝑝 𝑟 {\displaystyle{\displaystyle d_{m,p}^{(r)}}}
    xml-id
    C22.S9.XMD5.m1jdec
    0 references
    change of variable
    DLMF defining formula
    κ 𝜅 {\displaystyle{\displaystyle\kappa}}
    xml-id
    C22.S9.XMD6.m1hdec
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    Identifiers

     
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