DLMF:13.20.E14 (Q4603): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q10816 / rank
 
Normal rank
Property / Symbols used: Q10816 / qualifier
 
test:

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

\atan@@{\NVar{z}}
Property / Symbols used: Q10816 / qualifier
 
xml-id: C4.S23.SS2.p1.m7adec
Property / Symbols used
 
Property / Symbols used: Q11566 / rank
 
Normal rank
Property / Symbols used: Q11566 / qualifier
 
test:

x 𝑥 {\displaystyle{\displaystyle x}}

x
Property / Symbols used: Q11566 / qualifier
 
xml-id: C13.S1.XMD4.m1kdec
Property / Symbols used
 
Property / Symbols used: DLMF:13.20.E6 / rank
 
Normal rank
Property / Symbols used: DLMF:13.20.E6 / qualifier
 
test:

α 𝛼 {\displaystyle{\displaystyle\alpha}}

\alpha
Property / Symbols used: DLMF:13.20.E6 / qualifier
 
xml-id: C13.S20.XMD2.m1cdec
Property / Symbols used
 
Property / Symbols used: DLMF:13.20.E7 / rank
 
Normal rank
Property / Symbols used: DLMF:13.20.E7 / qualifier
 
test:

X 𝑋 {\displaystyle{\displaystyle X}}

X
Property / Symbols used: DLMF:13.20.E7 / qualifier
 
xml-id: C13.S20.XMD3.m1cdec

Latest revision as of 15:15, 2 January 2020

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DLMF:13.20.E14
No description defined

    Statements

    test
    ζ ⁢ α 2 - ζ 2 + α 2 ⁢ arcsin ⁡ ( ζ α ) = X μ + 2 ⁢ κ μ ⁢ arctan ⁡ ( x - 2 ⁢ κ X ) - 2 ⁢ arctan ⁡ ( κ ⁢ x - 2 ⁢ μ 2 μ ⁢ X ) , 𝜁 superscript 𝛼 2 superscript 𝜁 2 superscript 𝛼 2 𝜁 𝛼 𝑋 𝜇 2 𝜅 𝜇 𝑥 2 𝜅 𝑋 2 𝜅 𝑥 2 superscript 𝜇 2 𝜇 𝑋 {\displaystyle{\displaystyle\zeta\sqrt{\alpha^{2}-\zeta^{2}}+\alpha^{2}% \operatorname{arcsin}\left(\frac{\zeta}{\alpha}\right)=\frac{X}{\mu}+\frac{2% \kappa}{\mu}\operatorname{arctan}\left(\frac{x-2\kappa}{X}\right)-2% \operatorname{arctan}\left(\frac{\kappa x-2\mu^{2}}{\mu X}\right),}}
    0 references
    DLMF id
    DLMF:13.20.E14
    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\leq 2% \kappa+2\sqrt{\kappa^{2}-\mu^{2}}}}
    0 references
    Symbols used
    Q11242
    test
    arcsin ⁡ z 𝑧 {\displaystyle{\displaystyle\operatorname{arcsin}\NVar{z}}}
    xml-id
    C4.S23.SS2.p1.m5adec
    0 references
    Q10816
    test
    arctan ⁡ z 𝑧 {\displaystyle{\displaystyle\operatorname{arctan}\NVar{z}}}
    xml-id
    C4.S23.SS2.p1.m7adec
    0 references
    Q11566
    test
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C13.S1.XMD4.m1kdec
    0 references
    DLMF:13.20.E6
    test
    α 𝛼 {\displaystyle{\displaystyle\alpha}}
    xml-id
    C13.S20.XMD2.m1cdec
    0 references
    DLMF:13.20.E7
    test
    X 𝑋 {\displaystyle{\displaystyle X}}
    xml-id
    C13.S20.XMD3.m1cdec
    0 references
     
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