DLMF:19.2.E22 (Q6118): Difference between revisions

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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.m2aedec
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.m2acdec
Property / Symbols used
 
Property / Symbols used: cosine function / rank
 
Normal rank
Property / Symbols used: cosine function / qualifier
 
test:

cos z 𝑧 {\displaystyle{\displaystyle\cos\NVar{z}}}

\cos@@{\NVar{z}}
Property / Symbols used: cosine function / qualifier
 
xml-id: C4.S14.E2.m2abdec
Property / Symbols used
 
Property / Symbols used: Q10770 / rank
 
Normal rank
Property / Symbols used: Q10770 / qualifier
 
test:

d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}

\diff{\NVar{x}}
Property / Symbols used: Q10770 / qualifier
 
xml-id: C1.S4.SS4.m1akdec
Property / Symbols used
 
Property / Symbols used: Q10771 / rank
 
Normal rank
Property / Symbols used: Q10771 / qualifier
 
test:

{\displaystyle{\displaystyle\int}}

\int
Property / Symbols used: Q10771 / qualifier
 
xml-id: C1.S4.SS4.m3akdec
Property / Symbols used
 
Property / Symbols used: sine function / rank
 
Normal rank
Property / Symbols used: sine function / qualifier
 
test:

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

\sin@@{\NVar{z}}
Property / Symbols used: sine function / qualifier
 
xml-id: C4.S14.E1.m2afdec

Latest revision as of 12:36, 2 January 2020

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DLMF:19.2.E22
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    Statements

    R C ( x , y ) = 2 π 0 π / 2 R C ( y , x cos 2 θ + y sin 2 θ ) d θ . Carlson-integral-RC 𝑥 𝑦 2 𝜋 superscript subscript 0 𝜋 2 Carlson-integral-RC 𝑦 𝑥 2 𝜃 𝑦 2 𝜃 𝜃 {\displaystyle{\displaystyle R_{C}\left(x,y\right)=\frac{2}{\pi}\int_{0}^{\pi/% 2}R_{C}\left(y,x{\cos^{2}}\theta+y{\sin^{2}}\theta\right)\mathrm{d}\theta.}}
    0 references
    0 references
    R C ( x , y ) Carlson-integral-RC 𝑥 𝑦 {\displaystyle{\displaystyle R_{C}\left(\NVar{x},\NVar{y}\right)}}
    C19.S2.E17.m2aedec
    0 references
    π {\displaystyle{\displaystyle\pi}}
    C3.S12.E1.m2acdec
    0 references
    cos z 𝑧 {\displaystyle{\displaystyle\cos\NVar{z}}}
    C4.S14.E2.m2abdec
    0 references
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    C1.S4.SS4.m1akdec
    0 references
    {\displaystyle{\displaystyle\int}}
    C1.S4.SS4.m3akdec
    0 references
    sin z 𝑧 {\displaystyle{\displaystyle\sin\NVar{z}}}
    C4.S14.E1.m2afdec
    0 references