DLMF:19.12.E7 (Q6305): Difference between revisions

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‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
Property / Symbols used
 
Property / Symbols used: Carlson’s combination of inverse circular and inverse hyperbolic functions / rank
 
Normal rank
Property / Symbols used: Carlson’s combination of inverse circular and inverse hyperbolic functions / qualifier
 
Defining formula:

R C ⁡ ( x , y ) Carlson-integral-RC 𝑥 𝑦 {\displaystyle{\displaystyle R_{C}\left(\NVar{x},\NVar{y}\right)}}

\CarlsonellintRC@{\NVar{x}}{\NVar{y}}
Property / Symbols used: Carlson’s combination of inverse circular and inverse hyperbolic functions / qualifier
 
xml-id: C19.S2.E17.m2acdec

Revision as of 13:50, 2 January 2020

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DLMF:19.12.E7
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    Statements

    Defining formula
    R C ⁡ ( x , y ) = 1 2 ⁢ x ⁢ ( ( 1 + y 2 ⁢ x ) ⁢ ln ⁡ ( 4 ⁢ x y ) - y 2 ⁢ x ) ⁢ ( 1 + O ⁡ ( y 2 / x 2 ) ) , Carlson-integral-RC 𝑥 𝑦 1 2 𝑥 1 𝑦 2 𝑥 4 𝑥 𝑦 𝑦 2 𝑥 1 Big-O superscript 𝑦 2 superscript 𝑥 2 {\displaystyle{\displaystyle R_{C}\left(x,y\right)=\frac{1}{2\sqrt{x}}\left(% \left(1+\frac{y}{2x}\right)\ln\left(\frac{4x}{y}\right)-\frac{y}{2x}\right)\*(% 1+O\left(y^{2}/x^{2}\right)),}}
    0 references
    DLMF id
    DLMF:19.12.E7
    0 references
    constraint
    y / x → 0 → 𝑦 𝑥 0 {\displaystyle{\displaystyle y/x\to 0}}
    0 references
    Symbols used
    order not exceeding
    Defining formula
    O ⁡ ( x ) Big-O 𝑥 {\displaystyle{\displaystyle O\left(\NVar{x}\right)}}
    xml-id
    C2.S1.E3.m2acdec
    0 references
    Carlson’s combination of inverse circular and inverse hyperbolic functions
    Defining formula
    R C ⁡ ( x , y ) Carlson-integral-RC 𝑥 𝑦 {\displaystyle{\displaystyle R_{C}\left(\NVar{x},\NVar{y}\right)}}
    xml-id
    C19.S2.E17.m2acdec
    0 references
     
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