DLMF:19.27.E16 (Q6608): Difference between revisions

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Property / constraint
 

max ⁡ ( y , z , p ) / x → 0 → 𝑦 𝑧 𝑝 𝑥 0 {\displaystyle{\displaystyle\max(y,z,p)/x\to 0}}

\max(y,z,p)/x\to 0
Property / constraint: max ⁡ ( y , z , p ) / x → 0 → 𝑦 𝑧 𝑝 𝑥 0 {\displaystyle{\displaystyle\max(y,z,p)/x\to 0}} / rank
 
Normal rank
Property / Symbols used
 
Property / Symbols used: order not exceeding / rank
 
Normal rank
Property / Symbols used: order not exceeding / qualifier
 
Defining formula:

O ⁡ ( x ) Big-O 𝑥 {\displaystyle{\displaystyle O\left(\NVar{x}\right)}}

\bigO@{\NVar{x}}
Property / Symbols used: order not exceeding / qualifier
 
xml-id: C2.S1.E3.m2andec
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.m2abdec
Property / Symbols used
 
Property / Symbols used: symmetric elliptic integral of third kind / rank
 
Normal rank
Property / Symbols used: symmetric elliptic integral of third kind / qualifier
 
Defining formula:

R J ⁡ ( x , y , z , p ) Carlson-integral-RJ 𝑥 𝑦 𝑧 𝑝 {\displaystyle{\displaystyle R_{J}\left(\NVar{x},\NVar{y},\NVar{z},\NVar{p}% \right)}}

\CarlsonsymellintRJ@{\NVar{x}}{\NVar{y}}{\NVar{z}}{\NVar{p}}
Property / Symbols used: symmetric elliptic integral of third kind / qualifier
 
xml-id: C19.S16.E2.m2aedec
Property / Symbols used
 
Property / Symbols used: principal branch of logarithm function / rank
 
Normal rank
Property / Symbols used: principal branch of logarithm function / qualifier
 
Defining formula:

ln ⁡ z 𝑧 {\displaystyle{\displaystyle\ln\NVar{z}}}

\ln@@{\NVar{z}}
Property / Symbols used: principal branch of logarithm function / qualifier
 
xml-id: C4.S2.E2.m2agdec
Property / Symbols used
 
Property / Symbols used: Q11891 / rank
 
Normal rank
Property / Symbols used: Q11891 / qualifier
 
Defining formula:

b 𝑏 {\displaystyle{\displaystyle b}}

b
Property / Symbols used: Q11891 / qualifier
 
xml-id: C19.S27.XMD2.m1cdec
Property / Symbols used
 
Property / Symbols used: Q11890 / rank
 
Normal rank
Property / Symbols used: Q11890 / qualifier
 
Defining formula:

h ℎ {\displaystyle{\displaystyle h}}

h
Property / Symbols used: Q11890 / qualifier
 
xml-id: C19.S27.XMD6.m1edec

Latest revision as of 14:16, 2 January 2020

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English
DLMF:19.27.E16
No description defined

    Statements

    Defining formula
    R J ⁡ ( x , y , z , p ) = ( 3 / x ) ⁢ R C ⁡ ( ( h + p ) 2 , 2 ⁢ ( b + h ) ⁢ p ) + O ⁡ ( 1 x 3 / 2 ⁢ ln ⁡ x b + h ) , Carlson-integral-RJ 𝑥 𝑦 𝑧 𝑝 3 𝑥 Carlson-integral-RC superscript ℎ 𝑝 2 2 𝑏 ℎ 𝑝 Big-O 1 superscript 𝑥 3 2 𝑥 𝑏 ℎ {\displaystyle{\displaystyle R_{J}\left(x,y,z,p\right)=(3/\sqrt{x})R_{C}\left(% (h+p)^{2},2(b+h)p\right)+O\left(\frac{1}{x^{3/2}}\ln\frac{x}{b+h}\right),}}
    0 references
    DLMF id
    DLMF:19.27.E16
    0 references
    constraint
    max ⁡ ( y , z , p ) / x → 0 → 𝑦 𝑧 𝑝 𝑥 0 {\displaystyle{\displaystyle\max(y,z,p)/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.m2andec
    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.m2abdec
    0 references
    symmetric elliptic integral of third kind
    Defining formula
    R J ⁡ ( x , y , z , p ) Carlson-integral-RJ 𝑥 𝑦 𝑧 𝑝 {\displaystyle{\displaystyle R_{J}\left(\NVar{x},\NVar{y},\NVar{z},\NVar{p}% \right)}}
    xml-id
    C19.S16.E2.m2aedec
    0 references
    principal branch of logarithm function
    Defining formula
    ln ⁡ z 𝑧 {\displaystyle{\displaystyle\ln\NVar{z}}}
    xml-id
    C4.S2.E2.m2agdec
    0 references
    Q11891
    Defining formula
    b 𝑏 {\displaystyle{\displaystyle b}}
    xml-id
    C19.S27.XMD2.m1cdec
    0 references
    Q11890
    Defining formula
    h ℎ {\displaystyle{\displaystyle h}}
    xml-id
    C19.S27.XMD6.m1edec
    0 references
     
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