DLMF:2.11.E11 (Q1036): Difference between revisions

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Property / Symbols defined
 
Property / Symbols defined: terminant function / rank
 
Normal rank
Property / Symbols used
 
Property / Symbols used: gamma function / rank
 
Normal rank
Property / Symbols used: gamma function / qualifier
 
test:

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.m2acdec
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
 
test:

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: Q10770 / rank
 
Normal rank
Property / Symbols used: Q10770 / qualifier
 
test:

d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}

\diff{\NVar{x}}
Property / Symbols used: Q10770 / qualifier
 
xml-id: C1.S4.SS4.m1abdec
Property / Symbols used
 
Property / Symbols used: base of natural logarithm / rank
 
Normal rank
Property / Symbols used: base of natural logarithm / qualifier
 
test:

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

\expe
Property / Symbols used: base of natural logarithm / qualifier
 
xml-id: C4.S2.E11.m2addec
Property / Symbols used
 
Property / Symbols used: generalized exponential integral / rank
 
Normal rank
Property / Symbols used: generalized exponential integral / qualifier
 
test:

E p ⁡ ( z ) exponential-integral-En 𝑝 𝑧 {\displaystyle{\displaystyle E_{\NVar{p}}\left(\NVar{z}\right)}}

\genexpintE{\NVar{p}}@{\NVar{z}}
Property / Symbols used: generalized exponential integral / qualifier
 
xml-id: C8.S19.E1.m2addec
Property / Symbols used
 
Property / Symbols used: Q10771 / rank
 
Normal rank
Property / Symbols used: Q10771 / qualifier
 
test:

∫ {\displaystyle{\displaystyle\int}}

\int
Property / Symbols used: Q10771 / qualifier
 
xml-id: C1.S4.SS4.m3abdec

Latest revision as of 16:39, 1 January 2020

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DLMF:2.11.E11
No description defined

    Statements

    test
    F n + p ⁡ ( z ) = e - z 2 ⁢ π ⁢ ∫ 0 ∞ e - z ⁢ t ⁢ t n + p - 1 1 + t ⁢ d t = Γ ⁡ ( n + p ) 2 ⁢ π ⁢ E n + p ⁡ ( z ) z n + p - 1 . terminant-function 𝑛 𝑝 𝑧 superscript 𝑒 𝑧 2 𝜋 superscript subscript 0 superscript 𝑒 𝑧 𝑡 superscript 𝑡 𝑛 𝑝 1 1 𝑡 𝑡 Euler-Gamma 𝑛 𝑝 2 𝜋 exponential-integral-En 𝑛 𝑝 𝑧 superscript 𝑧 𝑛 𝑝 1 {\displaystyle{\displaystyle F_{n+p}\left(z\right)=\frac{e^{-z}}{2\pi}\int_{0}% ^{\infty}\frac{e^{-zt}t^{n+p-1}}{1+t}\mathrm{d}t=\frac{\Gamma\left(n+p\right)}% {2\pi}\frac{E_{n+p}\left(z\right)}{z^{n+p-1}}.}}
    0 references
    DLMF id
    DLMF:2.11.E11
    0 references
    Symbols used
    gamma function
    test
    Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E1.m2acdec
    0 references
    the ratio of the circumference of a circle to its diameter
    test
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2addec
    0 references
    Q10770
    test
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1abdec
    0 references
    base of natural logarithm
    test
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2addec
    0 references
    generalized exponential integral
    test
    E p ⁡ ( z ) exponential-integral-En 𝑝 𝑧 {\displaystyle{\displaystyle E_{\NVar{p}}\left(\NVar{z}\right)}}
    xml-id
    C8.S19.E1.m2addec
    0 references
    Q10771
    test
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3abdec
    0 references
     
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