DLMF:2.11.E10 (Q1035): Difference between revisions

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‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
Property / Symbols used
 
Property / Symbols used: Q10759 / rank
 
Normal rank
Property / Symbols used: Q10759 / qualifier
 
Defining formula:

( 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.m1abdec

Revision as of 17:39, 1 January 2020

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DLMF:2.11.E10
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    Statements

    Defining formula
    E p ⁡ ( z ) = e - z z ⁢ ∑ s = 0 n - 1 ( - 1 ) s ⁢ ( p ) s z s + ( - 1 ) n ⁢ 2 ⁢ π Γ ⁡ ( p ) ⁢ z p - 1 ⁢ F n + p ⁡ ( z ) , exponential-integral-En 𝑝 𝑧 superscript 𝑒 𝑧 𝑧 superscript subscript 𝑠 0 𝑛 1 superscript 1 𝑠 Pochhammer 𝑝 𝑠 superscript 𝑧 𝑠 superscript 1 𝑛 2 𝜋 Euler-Gamma 𝑝 superscript 𝑧 𝑝 1 terminant-function 𝑛 𝑝 𝑧 {\displaystyle{\displaystyle E_{p}\left(z\right)=\frac{e^{-z}}{z}\sum_{s=0}^{n% -1}(-1)^{s}\frac{{\left(p\right)_{s}}}{z^{s}}+(-1)^{n}\frac{2\pi}{\Gamma\left(% p\right)}z^{p-1}F_{n+p}\left(z\right),}}
    0 references
    DLMF id
    DLMF:2.11.E10
    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.m2abdec
    0 references
    Q10759
    Defining formula
    ( a ) n Pochhammer 𝑎 𝑛 {\displaystyle{\displaystyle{\left(\NVar{a}\right)_{\NVar{n}}}}}
    xml-id
    C5.S2.SS3.m1abdec
    0 references
     
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