DLMF:19.28.E9 (Q6617): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q10771 / rank
 
Normal rank
Property / Symbols used: Q10771 / qualifier
 
Defining formula:

∫ {\displaystyle{\displaystyle\int}}

\int
Property / Symbols used: Q10771 / qualifier
 
xml-id: C1.S4.SS4.m3ahdec
Property / Symbols used
 
Property / Symbols used: sine function / rank
 
Normal rank
Property / Symbols used: sine function / qualifier
 
Defining formula:

sin ⁡ z 𝑧 {\displaystyle{\displaystyle\sin\NVar{z}}}

\sin@@{\NVar{z}}
Property / Symbols used: sine function / qualifier
 
xml-id: C4.S14.E1.m2adec

Latest revision as of 14:18, 2 January 2020

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DLMF:19.28.E9
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    Statements

    Defining formula
    ∫ 0 π / 2 R F ⁡ ( sin 2 ⁡ θ ⁢ cos 2 ⁡ ( x + y ) , sin 2 ⁡ θ ⁢ cos 2 ⁡ ( x - y ) , 1 ) ⁢ d θ = R F ⁡ ( 0 , cos 2 ⁡ x , 1 ) ⁢ R F ⁡ ( 0 , cos 2 ⁡ y , 1 ) , superscript subscript 0 𝜋 2 Carlson-integral-RF 2 𝜃 2 𝑥 𝑦 2 𝜃 2 𝑥 𝑦 1 𝜃 Carlson-integral-RF 0 2 𝑥 1 Carlson-integral-RF 0 2 𝑦 1 {\displaystyle{\displaystyle\int_{0}^{\pi/2}R_{F}\left({\sin^{2}}\theta{\cos^{% 2}}\left(x+y\right),{\sin^{2}}\theta{\cos^{2}}\left(x-y\right),1\right)\mathrm% {d}\theta=R_{F}\left(0,{\cos^{2}}x,1\right)R_{F}\left(0,{\cos^{2}}y,1\right),}}
    0 references
    DLMF id
    DLMF:19.28.E9
    0 references
    Symbols used
    symmetric elliptic integral of first kind
    Defining formula
    R F ⁡ ( x , y , z ) Carlson-integral-RF 𝑥 𝑦 𝑧 {\displaystyle{\displaystyle R_{F}\left(\NVar{x},\NVar{y},\NVar{z}\right)}}
    xml-id
    C19.S16.E1.m2addec
    0 references
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2aadec
    0 references
    cosine function
    Defining formula
    cos ⁡ z 𝑧 {\displaystyle{\displaystyle\cos\NVar{z}}}
    xml-id
    C4.S14.E2.m2adec
    0 references
    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1ahdec
    0 references
    Q10771
    Defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3ahdec
    0 references
    sine function
    Defining formula
    sin ⁡ z 𝑧 {\displaystyle{\displaystyle\sin\NVar{z}}}
    xml-id
    C4.S14.E1.m2adec
    0 references
     
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