DLMF:14.15.E21 (Q4867): Difference between revisions

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‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
 
Property / Symbols used
 
Property / Symbols used: Q11619 / rank
 
Normal rank
Property / Symbols used: Q11619 / qualifier
 
Defining formula:

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

\alpha
Property / Symbols used: Q11619 / qualifier
 
xml-id: C14.S15.XMD9.m1edec

Latest revision as of 01:52, 2 January 2020

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DLMF:14.15.E21
No description defined

    Statements

    Defining formula
    ( y - α 2 ) 1 / 2 - α ⁢ arctan ⁡ ( ( y - α 2 ) 1 / 2 α ) = arccos ⁡ ( x ( 1 - α 2 ) 1 / 2 ) - α 2 ⁢ arccos ⁡ ( ( 1 + α 2 ) ⁢ x 2 - 1 + α 2 ( 1 - α 2 ) ⁢ ( 1 - x 2 ) ) , superscript 𝑦 superscript 𝛼 2 1 2 𝛼 superscript 𝑦 superscript 𝛼 2 1 2 𝛼 𝑥 superscript 1 superscript 𝛼 2 1 2 𝛼 2 1 superscript 𝛼 2 superscript 𝑥 2 1 superscript 𝛼 2 1 superscript 𝛼 2 1 superscript 𝑥 2 {\displaystyle{\displaystyle\left(y-\alpha^{2}\right)^{1/2}-\alpha% \operatorname{arctan}\left(\frac{\left(y-\alpha^{2}\right)^{1/2}}{\alpha}% \right)=\operatorname{arccos}\left(\frac{x}{\left(1-\alpha^{2}\right)^{1/2}}% \right)-\frac{\alpha}{2}\operatorname{arccos}\left(\frac{\left(1+\alpha^{2}% \right)x^{2}-1+\alpha^{2}}{\left(1-\alpha^{2}\right)\left(1-x^{2}\right)}% \right),}}
    0 references
    DLMF id
    DLMF:14.15.E21
    0 references
    constraint
    y ≥ α 2 𝑦 superscript 𝛼 2 {\displaystyle{\displaystyle y\geq\alpha^{2}}}
    0 references
    Symbols used
    Q11208
    Defining formula
    arccos ⁡ z 𝑧 {\displaystyle{\displaystyle\operatorname{arccos}\NVar{z}}}
    xml-id
    C4.S23.SS2.p1.m6adec
    0 references
    Q10816
    Defining formula
    arctan ⁡ z 𝑧 {\displaystyle{\displaystyle\operatorname{arctan}\NVar{z}}}
    xml-id
    C4.S23.SS2.p1.m7adec
    0 references
    Q11589
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C14.S1.XMD1.m1ldec
    0 references
    Q11618
    Defining formula
    y 𝑦 {\displaystyle{\displaystyle y}}
    xml-id
    C14.S15.XMD11.m1ddec
    0 references
    Q11619
    Defining formula
    α 𝛼 {\displaystyle{\displaystyle\alpha}}
    xml-id
    C14.S15.XMD9.m1edec
    0 references
     
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