DLMF:8.19.E27 (Q2713): Difference between revisions

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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.m3ahdec

Revision as of 13:13, 2 January 2020

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DLMF:8.19.E27
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    Statements

    test
    L ⁢ ( p ) = ∫ 0 ∞ e - t ⁢ E p ⁡ ( t ) ⁢ d t = 1 2 ⁢ p ⁢ F ⁡ ( 1 , 1 ; 1 + p ; 1 2 ) , 𝐿 𝑝 superscript subscript 0 superscript 𝑒 𝑡 exponential-integral-En 𝑝 𝑡 𝑡 1 2 𝑝 Gauss-hypergeometric-F 1 1 1 𝑝 1 2 {\displaystyle{\displaystyle L(p)=\int_{0}^{\infty}e^{-t}E_{p}\left(t\right)% \mathrm{d}t=\frac{1}{2p}F\left(1,1;1+p;\tfrac{1}{2}\right),}}
    0 references
    DLMF id
    DLMF:8.19.E27
    0 references
    constraint
    p > 0 𝑝 0 {\displaystyle{\displaystyle p>0}}
    0 references
    Symbols used
    $$={{}_{2}F_{1}}\left(\NVar{a},\NVar{b};\NVar{c};\NVar{z}\right)$$ Gauss’ hypergeometric function
    test
    F ⁡ ( a , b ; c ; z ) Gauss-hypergeometric-F 𝑎 𝑏 𝑐 𝑧 {\displaystyle{\displaystyle F\left(\NVar{a},\NVar{b};\NVar{c};\NVar{z}\right)}}
    xml-id
    C15.S2.E1.m2aadec
    0 references
    Q10770
    test
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1ahdec
    0 references
    base of natural logarithm
    test
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2apdec
    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.m2aaedec
    0 references
    Q10771
    test
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3ahdec
    0 references
     
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