DLMF:8.8.E19 (Q2551): Difference between revisions

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‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
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 𝑎 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{a},\NVar{z}\right)}}

\incGamma@{\NVar{a}}{\NVar{z}}
Property / Symbols used: incomplete gamma function / qualifier
 
xml-id: C8.S2.E2.m2aedec

Revision as of 13:50, 2 January 2020

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DLMF:8.8.E19
No description defined

    Statements

    Defining formula
    d n d z n ⁡ ( e z ⁢ Γ ⁡ ( a , z ) ) = ( - 1 ) n ⁢ ( 1 - a ) n ⁢ e z ⁢ Γ ⁡ ( a - n , z ) . derivative 𝑧 𝑛 superscript 𝑒 𝑧 incomplete-Gamma 𝑎 𝑧 superscript 1 𝑛 Pochhammer 1 𝑎 𝑛 superscript 𝑒 𝑧 incomplete-Gamma 𝑎 𝑛 𝑧 {\displaystyle{\displaystyle\frac{{\mathrm{d}}^{n}}{{\mathrm{d}z}^{n}}(e^{z}% \Gamma\left(a,z\right))=(-1)^{n}{\left(1-a\right)_{n}}e^{z}\Gamma\left(a-n,z% \right).}}
    0 references
    DLMF id
    DLMF:8.8.E19
    0 references
    Symbols used
    Q10759
    Defining formula
    ( a ) n Pochhammer 𝑎 𝑛 {\displaystyle{\displaystyle{\left(\NVar{a}\right)_{\NVar{n}}}}}
    xml-id
    C5.S2.SS3.m1acdec
    0 references
    derivative of $$f$$ with respect to $$x$$
    Defining formula
    d f d x derivative 𝑓 𝑥 {\displaystyle{\displaystyle\frac{\mathrm{d}\NVar{f}}{\mathrm{d}\NVar{x}}}}
    xml-id
    C1.S4.E4.m2aedec
    0 references
    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2andec
    0 references
    incomplete gamma function
    Defining formula
    Γ ⁡ ( a , z ) incomplete-Gamma 𝑎 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{a},\NVar{z}\right)}}
    xml-id
    C8.S2.E2.m2aedec
    0 references
     
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