DLMF:19.4.E9 (Q6129): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q11815 / rank
 
Normal rank
Property / Symbols used: Q11815 / qualifier
 
Defining formula:

k ′ superscript 𝑘 ′ {\displaystyle{\displaystyle k^{\prime}}}

k^{\prime}
Property / Symbols used: Q11815 / qualifier
 
xml-id: C19.S1.XMD6.m1gdec

Revision as of 13:38, 2 January 2020

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DLMF:19.4.E9
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    Statements

    Defining formula
    ( k ⁢ k ′ 2 ⁢ D k 2 + k ′ 2 ⁢ D k + k ) ⁢ E ⁡ ( ϕ , k ) = k ⁢ sin ⁡ ϕ ⁢ cos ⁡ ϕ 1 - k 2 ⁢ sin 2 ⁡ ϕ . 𝑘 superscript superscript 𝑘 ′ 2 superscript subscript 𝐷 𝑘 2 superscript superscript 𝑘 ′ 2 subscript 𝐷 𝑘 𝑘 elliptic-integral-second-kind-E italic-ϕ 𝑘 𝑘 italic-ϕ italic-ϕ 1 superscript 𝑘 2 2 italic-ϕ {\displaystyle{\displaystyle(k{k^{\prime}}^{2}D_{k}^{2}+{k^{\prime}}^{2}D_{k}+% k)E\left(\phi,k\right)=\frac{k\sin\phi\cos\phi}{\sqrt{1-k^{2}{\sin^{2}}\phi}}.}}
    0 references
    DLMF id
    DLMF:19.4.E9
    0 references
    Symbols used
    cosine function
    Defining formula
    cos ⁡ z 𝑧 {\displaystyle{\displaystyle\cos\NVar{z}}}
    xml-id
    C4.S14.E2.m2acdec
    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.m2acdec
    0 references
    sine function
    Defining formula
    sin ⁡ z 𝑧 {\displaystyle{\displaystyle\sin\NVar{z}}}
    xml-id
    C4.S14.E1.m2acdec
    0 references
    Q11807
    Defining formula
    ϕ italic-ϕ {\displaystyle{\displaystyle\phi}}
    xml-id
    C19.S1.XMD4.m1ddec
    0 references
    Q11808
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C19.S1.XMD5.m1hdec
    0 references
    Q11815
    Defining formula
    k ′ superscript 𝑘 ′ {\displaystyle{\displaystyle k^{\prime}}}
    xml-id
    C19.S1.XMD6.m1gdec
    0 references
     
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