DLMF:2.11.E7 (Q1032): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q10759 / rank
 
Normal rank
Property / Symbols used: Q10759 / qualifier
 
test:

( a ) n Pochhammer 𝑎 𝑛 {\displaystyle{\displaystyle{\left(\NVar{a}\right)_{\NVar{n}}}}}

\Pochhammersym{\NVar{a}}{\NVar{n}}
Property / Symbols used: Q10759 / qualifier
 
xml-id: C5.S2.SS3.m1aadec
Property / Symbols used
 
Property / Symbols used: Q10931 / rank
 
Normal rank
Property / Symbols used: Q10931 / qualifier
 
test:

∼ asymptotic-expansion {\displaystyle{\displaystyle\sim}}

\asympexp
Property / Symbols used: Q10931 / qualifier
 
xml-id: C2.S1.SS3.p1.m11acdec
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.m2abdec
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.m2abdec
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.m2abdec
Property / Symbols used
 
Property / Symbols used: imaginary unit / rank
 
Normal rank
Property / Symbols used: imaginary unit / qualifier
 
test:

i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}

\iunit
Property / Symbols used: imaginary unit / qualifier
 
xml-id: C1.S9.E1.m2adec

Latest revision as of 16:39, 1 January 2020

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DLMF:2.11.E7
No description defined

    Statements

    test
    E p ⁡ ( z ) ∼ 2 ⁢ π ⁢ i ⁢ e - p ⁢ π ⁢ i Γ ⁡ ( p ) ⁢ z p - 1 + e - z z ⁢ ∑ s = 0 ∞ ( - 1 ) s ⁢ ( p ) s z s , asymptotic-expansion exponential-integral-En 𝑝 𝑧 2 𝜋 𝑖 superscript 𝑒 𝑝 𝜋 𝑖 Euler-Gamma 𝑝 superscript 𝑧 𝑝 1 superscript 𝑒 𝑧 𝑧 superscript subscript 𝑠 0 superscript 1 𝑠 Pochhammer 𝑝 𝑠 superscript 𝑧 𝑠 {\displaystyle{\displaystyle E_{p}\left(z\right)\sim\frac{2\pi ie^{-p\pi i}}{% \Gamma\left(p\right)}z^{p-1}+\frac{e^{-z}}{z}\sum_{s=0}^{\infty}(-1)^{s}\frac{% {\left(p\right)_{s}}}{z^{s}},}}
    0 references
    DLMF id
    DLMF:2.11.E7
    0 references
    Symbols used
    gamma function
    test
    Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E1.m2aadec
    0 references
    Q10759
    test
    ( a ) n Pochhammer 𝑎 𝑛 {\displaystyle{\displaystyle{\left(\NVar{a}\right)_{\NVar{n}}}}}
    xml-id
    C5.S2.SS3.m1aadec
    0 references
    Q10931
    test
    ∼ asymptotic-expansion {\displaystyle{\displaystyle\sim}}
    xml-id
    C2.S1.SS3.p1.m11acdec
    0 references
    the ratio of the circumference of a circle to its diameter
    test
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2abdec
    0 references
    base of natural logarithm
    test
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2abdec
    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.m2abdec
    0 references
    imaginary unit
    test
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2adec
    0 references
     
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