DLMF:14.20.E24 (Q4945): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q11636 / rank
 
Normal rank
Property / Symbols used: Q11636 / qualifier
 
test:

β 𝛽 {\displaystyle{\displaystyle\beta}}

\beta
Property / Symbols used: Q11636 / qualifier
 
xml-id: C14.S20.XMD8.m1bdec
Property / Symbols used
 
Property / Symbols used: Q11637 / rank
 
Normal rank
Property / Symbols used: Q11637 / qualifier
 
test:

ρ 𝜌 {\displaystyle{\displaystyle\rho}}

\rho
Property / Symbols used: Q11637 / qualifier
 
xml-id: C14.S20.XMD9.m1adec

Latest revision as of 12:37, 2 January 2020

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DLMF:14.20.E24
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    Statements

    test
    ρ = 1 2 ⁢ ln ⁡ ( ( 1 - β 2 ) ⁢ x 2 + 1 + β 2 + 2 ⁢ x ⁢ ( 1 + β 2 - β 2 ⁢ x 2 ) 1 / 2 1 - x 2 ) + β ⁢ arctan ⁡ ( β ⁢ x 1 + β 2 - β 2 ⁢ x 2 ) - 1 2 ⁢ ln ⁡ ( 1 + β 2 ) , 𝜌 1 2 1 superscript 𝛽 2 superscript 𝑥 2 1 superscript 𝛽 2 2 𝑥 superscript 1 superscript 𝛽 2 superscript 𝛽 2 superscript 𝑥 2 1 2 1 superscript 𝑥 2 𝛽 𝛽 𝑥 1 superscript 𝛽 2 superscript 𝛽 2 superscript 𝑥 2 1 2 1 superscript 𝛽 2 {\displaystyle{\displaystyle\rho=\frac{1}{2}\ln\left(\frac{\left(1-\beta^{2}% \right)x^{2}+1+\beta^{2}+2x\left(1+\beta^{2}-\beta^{2}x^{2}\right)^{1/2}}{1-x^% {2}}\right)+\beta\operatorname{arctan}\left(\frac{\beta x}{\sqrt{1+\beta^{2}-% \beta^{2}x^{2}}}\right)-\frac{1}{2}\ln\left(1+\beta^{2}\right),}}
    0 references
    DLMF id
    DLMF:14.20.E24
    0 references
    Symbols used
    Q10816
    test
    arctan ⁡ z 𝑧 {\displaystyle{\displaystyle\operatorname{arctan}\NVar{z}}}
    xml-id
    C4.S23.SS2.p1.m7abdec
    0 references
    principal branch of logarithm function
    test
    ln ⁡ z 𝑧 {\displaystyle{\displaystyle\ln\NVar{z}}}
    xml-id
    C4.S2.E2.m2aadec
    0 references
    Q11589
    test
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C14.S1.XMD1.m1xdec
    0 references
    Q11636
    test
    β 𝛽 {\displaystyle{\displaystyle\beta}}
    xml-id
    C14.S20.XMD8.m1bdec
    0 references
    Q11637
    test
    ρ 𝜌 {\displaystyle{\displaystyle\rho}}
    xml-id
    C14.S20.XMD9.m1adec
    0 references
     
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