DLMF:19.2.E5 (Q6086): Difference between revisions

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

sin ⁡ z 𝑧 {\displaystyle{\displaystyle\sin\NVar{z}}}

\sin@@{\NVar{z}}
Property / Symbols used: sine function / qualifier
 
xml-id: C4.S14.E1.m2aadec

Revision as of 13:34, 2 January 2020

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DLMF:19.2.E5
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    Statements

    Defining formula
    E ⁡ ( ϕ , k ) = ∫ 0 ϕ 1 - k 2 ⁢ sin 2 ⁡ θ ⁢ d θ = ∫ 0 sin ⁡ ϕ 1 - k 2 ⁢ t 2 1 - t 2 ⁢ d t . elliptic-integral-second-kind-E italic-ϕ 𝑘 superscript subscript 0 italic-ϕ 1 superscript 𝑘 2 2 𝜃 𝜃 superscript subscript 0 italic-ϕ 1 superscript 𝑘 2 superscript 𝑡 2 1 superscript 𝑡 2 𝑡 {\displaystyle{\displaystyle E\left(\phi,k\right)=\int_{0}^{\phi}\sqrt{1-k^{2}% {\sin^{2}}\theta}\mathrm{d}\theta\\ =\int_{0}^{\sin\phi}\frac{\sqrt{1-k^{2}t^{2}}}{\sqrt{1-t^{2}}}\mathrm{d}t.}}
    0 references
    DLMF id
    DLMF:19.2.E5
    0 references
    Symbols used
    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1acdec
    0 references
    Q10771
    Defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3acdec
    0 references
    sine function
    Defining formula
    sin ⁡ z 𝑧 {\displaystyle{\displaystyle\sin\NVar{z}}}
    xml-id
    C4.S14.E1.m2aadec
    0 references
     
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