DLMF:8.12.E6 (Q2601): 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.m2aadec
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.m2adec
Property / Symbols used
 
Property / Symbols used: base of natural logarithm / rank
 
Normal rank
Property / Symbols used: base of natural logarithm / qualifier
 
Defining formula:

e {\displaystyle{\displaystyle\mathrm{e}}}

\expe
Property / Symbols used: base of natural logarithm / qualifier
 
xml-id: C4.S2.E11.m2aadec
Property / Symbols used
 
Property / Symbols used: incomplete gamma function / rank
 
Normal rank
Property / Symbols used: incomplete gamma function / qualifier
 
Defining formula:

γ * ⁡ ( a , z ) incomplete-gamma-star 𝑎 𝑧 {\displaystyle{\displaystyle\gamma^{*}\left(\NVar{a},\NVar{z}\right)}}

\scincgamma@{\NVar{a}}{\NVar{z}}
Property / Symbols used: incomplete gamma function / qualifier
 
xml-id: C8.S2.E6.m2adec
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.m2aadec
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.m1ddec
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.m1ddec
Property / Symbols used
 
Property / Symbols used: Q11348 / rank
 
Normal rank
Property / Symbols used: Q11348 / qualifier
 
Defining formula:

η ⁢ ( λ ) 𝜂 𝜆 {\displaystyle{\displaystyle\eta(\lambda)}}

\eta(\lambda)
Property / Symbols used: Q11348 / qualifier
 
xml-id: C8.S12.XMD1.m1edec
Property / Symbols used
 
Property / Symbols used: Q11350 / rank
 
Normal rank
Property / Symbols used: Q11350 / qualifier
 
Defining formula:

T ⁢ ( a , η ) 𝑇 𝑎 𝜂 {\displaystyle{\displaystyle T(a,\eta)}}

T(a,\eta)
Property / Symbols used: Q11350 / qualifier
 
xml-id: C8.S12.XMD4.m1adec

Latest revision as of 13:57, 2 January 2020

No description defined
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DLMF:8.12.E6
No description defined

    Statements

    Defining formula
    z - a ⁢ γ * ⁡ ( - a , - z ) = cos ⁡ ( π ⁢ a ) - 2 ⁢ sin ⁡ ( π ⁢ a ) ⁢ ( e 1 2 ⁢ a ⁢ η 2 π ⁢ F ⁡ ( η ⁢ a / 2 ) + T ⁢ ( a , η ) ) , superscript 𝑧 𝑎 incomplete-gamma-star 𝑎 𝑧 𝜋 𝑎 2 𝜋 𝑎 superscript 𝑒 1 2 𝑎 superscript 𝜂 2 𝜋 Dawsons-integral 𝜂 𝑎 2 𝑇 𝑎 𝜂 {\displaystyle{\displaystyle z^{-a}\gamma^{*}\left(-a,-z\right)=\cos\left(\pi a% \right)-2\sin\left(\pi a\right)\left(\frac{e^{\frac{1}{2}a\eta^{2}}}{\sqrt{\pi% }}F\left(\eta\sqrt{a/2}\right)+T(a,\eta)\right),}}
    0 references
    DLMF id
    DLMF:8.12.E6
    0 references
    Symbols used
    Dawson’s integral
    Defining formula
    F ⁡ ( z ) Dawsons-integral 𝑧 {\displaystyle{\displaystyle F\left(\NVar{z}\right)}}
    xml-id
    C7.S2.E5.m2adec
    0 references
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2aadec
    0 references
    cosine function
    Defining formula
    cos ⁡ z 𝑧 {\displaystyle{\displaystyle\cos\NVar{z}}}
    xml-id
    C4.S14.E2.m2adec
    0 references
    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2aadec
    0 references
    incomplete gamma function
    Defining formula
    γ * ⁡ ( a , z ) incomplete-gamma-star 𝑎 𝑧 {\displaystyle{\displaystyle\gamma^{*}\left(\NVar{a},\NVar{z}\right)}}
    xml-id
    C8.S2.E6.m2adec
    0 references
    sine function
    Defining formula
    sin ⁡ z 𝑧 {\displaystyle{\displaystyle\sin\NVar{z}}}
    xml-id
    C4.S14.E1.m2aadec
    0 references
    Q11323
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C8.S1.XMD2.m1ddec
    0 references
    Q11324
    Defining formula
    a 𝑎 {\displaystyle{\displaystyle a}}
    xml-id
    C8.S1.XMD3.m1ddec
    0 references
    Q11348
    Defining formula
    η ⁢ ( λ ) 𝜂 𝜆 {\displaystyle{\displaystyle\eta(\lambda)}}
    xml-id
    C8.S12.XMD1.m1edec
    0 references
    Q11350
    Defining formula
    T ⁢ ( a , η ) 𝑇 𝑎 𝜂 {\displaystyle{\displaystyle T(a,\eta)}}
    xml-id
    C8.S12.XMD4.m1adec
    0 references
     
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