DLMF:19.11.E13 (Q6288)

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DLMF:19.11.E13
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    Statements

    Defining formula
    E ⁡ ( ψ , k ) = 2 ⁢ E ⁡ ( θ , k ) - k 2 ⁢ sin 2 ⁡ θ ⁢ sin ⁡ ψ , elliptic-integral-second-kind-E 𝜓 𝑘 2 elliptic-integral-second-kind-E 𝜃 𝑘 superscript 𝑘 2 2 𝜃 𝜓 {\displaystyle{\displaystyle E\left(\psi,k\right)=2E\left(\theta,k\right)-k^{2% }{\sin^{2}}\theta\sin\psi,}}
    0 references
    DLMF id
    DLMF:19.11.E13
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    Symbols used
    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.m2abdec
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    sine function
    Defining formula
    sin ⁡ z 𝑧 {\displaystyle{\displaystyle\sin\NVar{z}}}
    xml-id
    C4.S14.E1.m2addec
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    Q11808
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C19.S1.XMD5.m1kdec
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    Q11842
    Defining formula
    θ 𝜃 {\displaystyle{\displaystyle\theta}}
    xml-id
    C19.S11.XMD1.m1ldec
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    angle (locally)
    Defining formula
    ψ 𝜓 {\displaystyle{\displaystyle\psi}}
    xml-id
    C19.S11.XMD8.m1adec
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