DLMF:8.21.E8 (Q2729): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: generalized sine integral / rank
 
Normal rank
Property / Symbols used: generalized sine integral / qualifier
 
Defining formula:

Si ⁡ ( a , z ) generalized-sine-integral-Si 𝑎 𝑧 {\displaystyle{\displaystyle\mathrm{Si}\left(\NVar{a},\NVar{z}\right)}}

\gensinint@{\NVar{a}}{\NVar{z}}
Property / Symbols used: generalized sine integral / qualifier
 
xml-id: C8.S21.E2.m3abdec
Property / Symbols used
 
Property / Symbols used: generalized sine integral / rank
 
Normal rank
Property / Symbols used: generalized sine integral / qualifier
 
Defining formula:

si ⁡ ( a , z ) generalized-sine-integral-si 𝑎 𝑧 {\displaystyle{\displaystyle\mathrm{si}\left(\NVar{a},\NVar{z}\right)}}

\genshiftsinint@{\NVar{a}}{\NVar{z}}
Property / Symbols used: generalized sine integral / qualifier
 
xml-id: C8.S21.E1.m3abdec
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.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.m1fdec
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.m1gdec

Latest revision as of 14:16, 2 January 2020

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DLMF:8.21.E8
No description defined

    Statements

    Defining formula
    Si ⁡ ( a , z ) = Γ ⁡ ( a ) ⁢ sin ⁡ ( 1 2 ⁢ π ⁢ a ) - si ⁡ ( a , z ) , generalized-sine-integral-Si 𝑎 𝑧 Euler-Gamma 𝑎 1 2 𝜋 𝑎 generalized-sine-integral-si 𝑎 𝑧 {\displaystyle{\displaystyle\mathrm{Si}\left(a,z\right)=\Gamma\left(a\right)% \sin\left(\tfrac{1}{2}\pi a\right)-\mathrm{si}\left(a,z\right),}}
    0 references
    DLMF id
    DLMF:8.21.E8
    0 references
    constraint
    a ≠ - 1 , - 3 , - 5 , … 𝑎 1 3 5 … {\displaystyle{\displaystyle a\neq-1,-3,-5,\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.m2aadec
    0 references
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2acdec
    0 references
    generalized sine integral
    Defining formula
    Si ⁡ ( a , z ) generalized-sine-integral-Si 𝑎 𝑧 {\displaystyle{\displaystyle\mathrm{Si}\left(\NVar{a},\NVar{z}\right)}}
    xml-id
    C8.S21.E2.m3abdec
    0 references
    generalized sine integral
    Defining formula
    si ⁡ ( a , z ) generalized-sine-integral-si 𝑎 𝑧 {\displaystyle{\displaystyle\mathrm{si}\left(\NVar{a},\NVar{z}\right)}}
    xml-id
    C8.S21.E1.m3abdec
    0 references
    sine function
    Defining formula
    sin ⁡ z 𝑧 {\displaystyle{\displaystyle\sin\NVar{z}}}
    xml-id
    C4.S14.E1.m2abdec
    0 references
    Q11323
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C8.S1.XMD2.m1fdec
    0 references
    Q11324
    Defining formula
    a 𝑎 {\displaystyle{\displaystyle a}}
    xml-id
    C8.S1.XMD3.m1gdec
    0 references
     
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