DLMF:19.25.E7 (Q6511): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q11808 / rank
 
Normal rank
Property / Symbols used: Q11808 / qualifier
 
Defining formula:

k 𝑘 {\displaystyle{\displaystyle k}}

k
Property / Symbols used: Q11808 / qualifier
 
xml-id: C19.S1.XMD5.m1fdec

Latest revision as of 14:05, 2 January 2020

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DLMF:19.25.E7
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    Statements

    Defining formula
    E ⁡ ( ϕ , k ) = 2 ⁢ R G ⁡ ( c - 1 , c - k 2 , c ) - ( c - 1 ) ⁢ R F ⁡ ( c - 1 , c - k 2 , c ) - ( c - 1 ) ⁢ ( c - k 2 ) / c , elliptic-integral-second-kind-E italic-ϕ 𝑘 2 Carlson-integral-RG 𝑐 1 𝑐 superscript 𝑘 2 𝑐 𝑐 1 Carlson-integral-RF 𝑐 1 𝑐 superscript 𝑘 2 𝑐 𝑐 1 𝑐 superscript 𝑘 2 𝑐 {\displaystyle{\displaystyle E\left(\phi,k\right)=2R_{G}\left(c-1,c-k^{2},c% \right)-(c-1)R_{F}\left(c-1,c-k^{2},c\right)-\sqrt{(c-1)(c-k^{2})/c},}}
    0 references
    DLMF id
    DLMF:19.25.E7
    0 references
    Symbols used
    symmetric elliptic integral of first kind
    Defining formula
    R F ⁡ ( x , y , z ) Carlson-integral-RF 𝑥 𝑦 𝑧 {\displaystyle{\displaystyle R_{F}\left(\NVar{x},\NVar{y},\NVar{z}\right)}}
    xml-id
    C19.S16.E1.m2abdec
    0 references
    symmetric elliptic integral of second kind
    Defining formula
    R G ⁡ ( x , y , z ) Carlson-integral-RG 𝑥 𝑦 𝑧 {\displaystyle{\displaystyle R_{G}\left(\NVar{x},\NVar{y},\NVar{z}\right)}}
    xml-id
    C19.S16.E3.m2aadec
    0 references
    Legendre’s incomplete elliptic integral of the second kind
    Defining formula
    E ⁡ ( ϕ , k ) elliptic-integral-second-kind-E italic-ϕ 𝑘 {\displaystyle{\displaystyle E\left(\NVar{\phi},\NVar{k}\right)}}
    xml-id
    C19.S2.E5.m2adec
    0 references
    Q11807
    Defining formula
    ϕ italic-ϕ {\displaystyle{\displaystyle\phi}}
    xml-id
    C19.S1.XMD4.m1bdec
    0 references
    Q11808
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C19.S1.XMD5.m1fdec
    0 references
     
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