DLMF:13.21.E12 (Q4620): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q11242 / rank
 
Normal rank
Property / Symbols used: Q11242 / qualifier
 
test:

arcsin ⁡ z 𝑧 {\displaystyle{\displaystyle\operatorname{arcsin}\NVar{z}}}

\asin@@{\NVar{z}}
Property / Symbols used: Q11242 / qualifier
 
xml-id: C4.S23.SS2.p1.m5adec

Revision as of 15:18, 2 January 2020

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DLMF:13.21.E12
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    Statements

    test
    κ ⁢ ζ - 4 ⁢ μ 2 - 2 ⁢ μ ⁢ arctan ⁡ ( κ ⁢ ζ - 4 ⁢ μ 2 2 ⁢ μ ) = 1 2 ⁢ ( X - π ⁢ μ ) - μ ⁢ arctan ⁡ ( x ⁢ κ - 2 ⁢ μ 2 μ ⁢ X ) + κ ⁢ arcsin ⁡ ( X 2 ⁢ κ 2 - μ 2 ) , 𝜅 𝜁 4 superscript 𝜇 2 2 𝜇 𝜅 𝜁 4 superscript 𝜇 2 2 𝜇 1 2 𝑋 𝜋 𝜇 𝜇 𝑥 𝜅 2 superscript 𝜇 2 𝜇 𝑋 𝜅 𝑋 2 superscript 𝜅 2 superscript 𝜇 2 {\displaystyle{\displaystyle\sqrt{\kappa\zeta-4\mu^{2}}-2\mu\operatorname{% arctan}\left(\frac{\sqrt{\kappa\zeta-4\mu^{2}}}{2\mu}\right)=\tfrac{1}{2}(X-% \pi\mu)-\mu\operatorname{arctan}\left(\frac{x\kappa-2\mu^{2}}{\mu X}\right)+% \kappa\operatorname{arcsin}\left(\frac{X}{2\sqrt{\kappa^{2}-\mu^{2}}}\right),}}
    0 references
    DLMF id
    DLMF:13.21.E12
    0 references
    constraint
    2 ⁢ κ - 2 ⁢ κ 2 - μ 2 ≤ x < 2 ⁢ κ + 2 ⁢ κ 2 - μ 2 2 𝜅 2 superscript 𝜅 2 superscript 𝜇 2 𝑥 2 𝜅 2 superscript 𝜅 2 superscript 𝜇 2 {\displaystyle{\displaystyle 2\kappa-2\sqrt{\kappa^{2}-\mu^{2}}\leq x<2\kappa+% 2\sqrt{\kappa^{2}-\mu^{2}}}}
    0 references
    Symbols used
    the ratio of the circumference of a circle to its diameter
    test
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2aedec
    0 references
    Q11242
    test
    arcsin ⁡ z 𝑧 {\displaystyle{\displaystyle\operatorname{arcsin}\NVar{z}}}
    xml-id
    C4.S23.SS2.p1.m5adec
    0 references
     
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