DLMF:19.26.E17 (Q6574): Difference between revisions

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Property / constraint
 

α , β ∈ ℂ ∖ ( - ∞ , 0 ) 𝛼 𝛽 0 {\displaystyle{\displaystyle\alpha,\beta\in\mathbb{C}\setminus(-\infty,0)}}

\alpha,\beta\in\Complexes\setminus(-\infty,0)
Property / constraint: α , β ∈ ℂ ∖ ( - ∞ , 0 ) 𝛼 𝛽 0 {\displaystyle{\displaystyle\alpha,\beta\in\mathbb{C}\setminus(-\infty,0)}} / rank
 
Normal rank
Property / constraint
 

α , β ∈ ℂ ∖ ( - ∞ , 0 ) 𝛼 𝛽 ℂ 0 {\displaystyle{\displaystyle\alpha,\beta\in\mathbb{C}\setminus(-\infty,0)}}

\alpha,\beta\in\mathbb{C}\setminus(-\infty,0)
Property / constraint: α , β ∈ ℂ ∖ ( - ∞ , 0 ) 𝛼 𝛽 ℂ 0 {\displaystyle{\displaystyle\alpha,\beta\in\mathbb{C}\setminus(-\infty,0)}} / rank
 
Normal rank
Property / constraint
 

α + β > 0 𝛼 𝛽 0 {\displaystyle{\displaystyle\alpha+\beta>0}}

\alpha+\beta>0
Property / constraint: α + β > 0 𝛼 𝛽 0 {\displaystyle{\displaystyle\alpha+\beta>0}} / rank
 
Normal rank
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
 
test:

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.m2addec
Property / Symbols used
 
Property / Symbols used: the ratio of the circumference of a circle to its diameter / rank
 
Normal rank
Property / Symbols used: the ratio of the circumference of a circle to its diameter / qualifier
 
test:

π {\displaystyle{\displaystyle\pi}}

\cpi
Property / Symbols used: the ratio of the circumference of a circle to its diameter / qualifier
 
xml-id: C3.S12.E1.m2adec
Property / Symbols used
 
Property / Symbols used: Q10923 / rank
 
Normal rank
Property / Symbols used: Q10923 / qualifier
 
test:

ℂ {\displaystyle{\displaystyle\mathbb{C}}}

\Complexes
Property / Symbols used: Q10923 / qualifier
 
xml-id: introduction.Sx4.p1.t1.r1.m2adec
Property / Symbols used
 
Property / Symbols used: Q10784 / rank
 
Normal rank
Property / Symbols used: Q10784 / qualifier
 
test:

∈ {\displaystyle{\displaystyle\in}}

\in
Property / Symbols used: Q10784 / qualifier
 
xml-id: introduction.Sx4.p1.t1.r10.m2aadec
Property / Symbols used
 
Property / Symbols used: Q10777 / rank
 
Normal rank
Property / Symbols used: Q10777 / qualifier
 
test:

( a , b ) 𝑎 𝑏 {\displaystyle{\displaystyle(\NVar{a},\NVar{b})}}

(\NVar{a},\NVar{b})
Property / Symbols used: Q10777 / qualifier
 
xml-id: introduction.Sx4.p1.t1.r29.m6adec
Property / Symbols used
 
Property / Symbols used: Q10785 / rank
 
Normal rank
Property / Symbols used: Q10785 / qualifier
 
test:

∖ {\displaystyle{\displaystyle\setminus}}

\setminus
Property / Symbols used: Q10785 / qualifier
 
xml-id: introduction.Sx4.p2.t1.r19.m2aadec
Property / Symbols used
 
Property / Symbols used: Q11809 / rank
 
Normal rank
Property / Symbols used: Q11809 / qualifier
 
test:

α 2 superscript 𝛼 2 {\displaystyle{\displaystyle\alpha^{2}}}

\alpha^{2}
Property / Symbols used: Q11809 / qualifier
 
xml-id: C19.S1.XMD7.m1adec

Latest revision as of 13:13, 2 January 2020

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DLMF:19.26.E17
No description defined

    Statements

    test
    α ⁢ R C ⁡ ( β , α + β ) + β ⁢ R C ⁡ ( α , α + β ) = π / 2 , 𝛼 Carlson-integral-RC 𝛽 𝛼 𝛽 𝛽 Carlson-integral-RC 𝛼 𝛼 𝛽 𝜋 2 {\displaystyle{\displaystyle\sqrt{\alpha}R_{C}\left(\beta,\alpha+\beta\right)+% \sqrt{\beta}R_{C}\left(\alpha,\alpha+\beta\right)=\pi/2,}}
    0 references
    DLMF id
    DLMF:19.26.E17
    0 references
    constraint
    α , β ∈ ℂ ∖ ( - ∞ , 0 ) 𝛼 𝛽 0 {\displaystyle{\displaystyle\alpha,\beta\in\mathbb{C}\setminus(-\infty,0)}}
    0 references
    α , β ∈ ℂ ∖ ( - ∞ , 0 ) 𝛼 𝛽 ℂ 0 {\displaystyle{\displaystyle\alpha,\beta\in\mathbb{C}\setminus(-\infty,0)}}
    0 references
    α + β > 0 𝛼 𝛽 0 {\displaystyle{\displaystyle\alpha+\beta>0}}
    0 references
    Symbols used
    Carlson’s combination of inverse circular and inverse hyperbolic functions
    test
    R C ⁡ ( x , y ) Carlson-integral-RC 𝑥 𝑦 {\displaystyle{\displaystyle R_{C}\left(\NVar{x},\NVar{y}\right)}}
    xml-id
    C19.S2.E17.m2addec
    0 references
    the ratio of the circumference of a circle to its diameter
    test
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2adec
    0 references
    Q10923
    test
    ℂ {\displaystyle{\displaystyle\mathbb{C}}}
    xml-id
    introduction.Sx4.p1.t1.r1.m2adec
    0 references
    Q10784
    test
    ∈ {\displaystyle{\displaystyle\in}}
    xml-id
    introduction.Sx4.p1.t1.r10.m2aadec
    0 references
    Q10777
    test
    ( a , b ) 𝑎 𝑏 {\displaystyle{\displaystyle(\NVar{a},\NVar{b})}}
    xml-id
    introduction.Sx4.p1.t1.r29.m6adec
    0 references
    Q10785
    test
    ∖ {\displaystyle{\displaystyle\setminus}}
    xml-id
    introduction.Sx4.p2.t1.r19.m2aadec
    0 references
    Q11809
    test
    α 2 superscript 𝛼 2 {\displaystyle{\displaystyle\alpha^{2}}}
    xml-id
    C19.S1.XMD7.m1adec
    0 references
     
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