DLMF:8.21.E13 (Q2735): Difference between revisions

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Property / constraint
 

a 0 , - 2 , - 4 , 𝑎 0 2 4 {\displaystyle{\displaystyle a\neq 0,-2,-4,\dots}}

a\neq 0,-2,-4,\dots
Property / constraint: a 0 , - 2 , - 4 , 𝑎 0 2 4 {\displaystyle{\displaystyle a\neq 0,-2,-4,\dots}} / rank
 
Normal rank
Property / Symbols used
 
Property / Symbols used: gamma function / rank
 
Normal rank
Property / Symbols used: gamma function / qualifier
 
Defining formula:

Γ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}

\EulerGamma@{\NVar{z}}
Property / Symbols used: gamma function / qualifier
 
xml-id: C5.S2.E1.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
 
Defining formula:

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.m2afdec
Property / Symbols used
 
Property / Symbols used: cosine function / rank
 
Normal rank
Property / Symbols used: cosine function / qualifier
 
Defining formula:

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

\cos@@{\NVar{z}}
Property / Symbols used: cosine function / qualifier
 
xml-id: C4.S14.E2.m2acdec
Property / Symbols used
 
Property / Symbols used: generalized cosine integral / rank
 
Normal rank
Property / Symbols used: generalized cosine integral / qualifier
 
Defining formula:

Ci ( a , z ) generalized-cosine-integral-Ci 𝑎 𝑧 {\displaystyle{\displaystyle\mathrm{Ci}\left(\NVar{a},\NVar{z}\right)}}

\gencosint@{\NVar{a}}{\NVar{z}}
Property / Symbols used: generalized cosine integral / qualifier
 
xml-id: C8.S21.E2.m2acdec
Property / Symbols used
 
Property / Symbols used: Q11324 / rank
 
Normal rank
Property / Symbols used: Q11324 / qualifier
 
Defining formula:

a 𝑎 {\displaystyle{\displaystyle a}}

a
Property / Symbols used: Q11324 / qualifier
 
xml-id: C8.S1.XMD3.m1jdec

Latest revision as of 14:17, 2 January 2020

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DLMF:8.21.E13
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    Statements

    Ci ( a , ) = Γ ( a ) cos ( 1 2 π a ) , generalized-cosine-integral-Ci 𝑎 Euler-Gamma 𝑎 1 2 𝜋 𝑎 {\displaystyle{\displaystyle\mathrm{Ci}\left(a,\infty\right)=\Gamma\left(a% \right)\cos\left(\tfrac{1}{2}\pi a\right),}}
    0 references
    DLMF:8.21.E13
    0 references
    a 0 , - 2 , - 4 , 𝑎 0 2 4 {\displaystyle{\displaystyle a\neq 0,-2,-4,\dots}}
    0 references
    Γ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    C5.S2.E1.m2addec
    0 references
    π {\displaystyle{\displaystyle\pi}}
    C3.S12.E1.m2afdec
    0 references
    cos z 𝑧 {\displaystyle{\displaystyle\cos\NVar{z}}}
    C4.S14.E2.m2acdec
    0 references
    Ci ( a , z ) generalized-cosine-integral-Ci 𝑎 𝑧 {\displaystyle{\displaystyle\mathrm{Ci}\left(\NVar{a},\NVar{z}\right)}}
    C8.S21.E2.m2acdec
    0 references
    a 𝑎 {\displaystyle{\displaystyle a}}
    C8.S1.XMD3.m1jdec
    0 references