DLMF:8.21.E9 (Q2730): Difference between revisions

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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.m2addec
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.m2abdec
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.m2abdec
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)}}

\genshiftcosint@{\NVar{a}}{\NVar{z}}
Property / Symbols used: generalized cosine integral / qualifier
 
xml-id: C8.S21.E1.m2abdec
Property / Symbols used
 
Property / Symbols used: Q11323 / rank
 
Normal rank
Property / Symbols used: Q11323 / qualifier
 
Defining formula:

z 𝑧 {\displaystyle{\displaystyle z}}

z
Property / Symbols used: Q11323 / qualifier
 
xml-id: C8.S1.XMD2.m1gdec
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.m1hdec

Latest revision as of 14:16, 2 January 2020

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DLMF:8.21.E9
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    Statements

    Defining formula
    Ci ⁡ ( a , z ) = Γ ⁡ ( a ) ⁢ cos ⁡ ( 1 2 ⁢ π ⁢ a ) - ci ⁡ ( a , z ) , generalized-cosine-integral-Ci 𝑎 𝑧 Euler-Gamma 𝑎 1 2 𝜋 𝑎 generalized-cosine-integral-ci 𝑎 𝑧 {\displaystyle{\displaystyle\mathrm{Ci}\left(a,z\right)=\Gamma\left(a\right)% \cos\left(\tfrac{1}{2}\pi a\right)-\mathrm{ci}\left(a,z\right),}}
    0 references
    DLMF id
    DLMF:8.21.E9
    0 references
    constraint
    a ≠ 0 , - 2 , - 4 , … 𝑎 0 2 4 … {\displaystyle{\displaystyle a\neq 0,-2,-4,\dots}}
    0 references
    Symbols used
    gamma function
    Defining formula
    Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E1.m2abdec
    0 references
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2addec
    0 references
    cosine function
    Defining formula
    cos ⁡ z 𝑧 {\displaystyle{\displaystyle\cos\NVar{z}}}
    xml-id
    C4.S14.E2.m2abdec
    0 references
    generalized cosine integral
    Defining formula
    Ci ⁡ ( a , z ) generalized-cosine-integral-Ci 𝑎 𝑧 {\displaystyle{\displaystyle\mathrm{Ci}\left(\NVar{a},\NVar{z}\right)}}
    xml-id
    C8.S21.E2.m2abdec
    0 references
    generalized cosine integral
    Defining formula
    ci ⁡ ( a , z ) generalized-cosine-integral-ci 𝑎 𝑧 {\displaystyle{\displaystyle\mathrm{ci}\left(\NVar{a},\NVar{z}\right)}}
    xml-id
    C8.S21.E1.m2abdec
    0 references
    Q11323
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C8.S1.XMD2.m1gdec
    0 references
    Q11324
    Defining formula
    a 𝑎 {\displaystyle{\displaystyle a}}
    xml-id
    C8.S1.XMD3.m1hdec
    0 references
     
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