DLMF:19.23.E5 (Q6476): Difference between revisions

From DRMF
Jump to navigation Jump to search
Changed an Item: Add constraint
Changed an Item: Add constraint
 
(One intermediate revision by the same user not shown)
Property / Symbols used
 
Property / Symbols used: Q10811 / rank
 
Normal rank
Property / Symbols used: Q10811 / qualifier
 
Defining formula:

absent {\displaystyle{\displaystyle\Re}}

\realpart@@
Property / Symbols used: Q10811 / qualifier
 
xml-id: C1.S9.E2.m1adec
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.m2acdec

Latest revision as of 14:02, 2 January 2020

No description defined
Language Label Description Also known as
English
DLMF:19.23.E5
No description defined

    Statements

    R F ( x , y , z ) = 2 π 0 π / 2 R C ( x , y cos 2 θ + z sin 2 θ ) d θ , Carlson-integral-RF 𝑥 𝑦 𝑧 2 𝜋 superscript subscript 0 𝜋 2 Carlson-integral-RC 𝑥 𝑦 2 𝜃 𝑧 2 𝜃 𝜃 {\displaystyle{\displaystyle R_{F}\left(x,y,z\right)=\frac{2}{\pi}\int_{0}^{% \pi/2}R_{C}\left(x,y{\cos^{2}}\theta+z{\sin^{2}}\theta\right)\mathrm{d}\theta,}}
    0 references
    DLMF:19.23.E5
    0 references
    y > 0 𝑦 0 {\displaystyle{\displaystyle\Re y>0}}
    0 references
    z > 0 𝑧 0 {\displaystyle{\displaystyle\Re z>0}}
    0 references
    R C ( x , y ) Carlson-integral-RC 𝑥 𝑦 {\displaystyle{\displaystyle R_{C}\left(\NVar{x},\NVar{y}\right)}}
    C19.S2.E17.m2aadec
    0 references
    R F ( x , y , z ) Carlson-integral-RF 𝑥 𝑦 𝑧 {\displaystyle{\displaystyle R_{F}\left(\NVar{x},\NVar{y},\NVar{z}\right)}}
    C19.S16.E1.m2abdec
    0 references
    π {\displaystyle{\displaystyle\pi}}
    C3.S12.E1.m2addec
    0 references
    cos z 𝑧 {\displaystyle{\displaystyle\cos\NVar{z}}}
    C4.S14.E2.m2addec
    0 references
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    C1.S4.SS4.m1addec
    0 references
    {\displaystyle{\displaystyle\int}}
    C1.S4.SS4.m3addec
    0 references
    absent {\displaystyle{\displaystyle\Re}}
    C1.S9.E2.m1adec
    0 references
    sin z 𝑧 {\displaystyle{\displaystyle\sin\NVar{z}}}
    C4.S14.E1.m2acdec
    0 references