DLMF:8.8.E16 (Q2548): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: derivative of $$f$$ with respect to $$x$$ / rank
 
Normal rank
Property / Symbols used: derivative of $$f$$ with respect to $$x$$ / qualifier
 
test:

d f d x derivative 𝑓 𝑥 {\displaystyle{\displaystyle\frac{\mathrm{d}\NVar{f}}{\mathrm{d}\NVar{x}}}}

\deriv{\NVar{f}}{\NVar{x}}
Property / Symbols used: derivative of $$f$$ with respect to $$x$$ / qualifier
 
xml-id: C1.S4.E4.m2abdec
Property / Symbols used
 
Property / Symbols used: incomplete gamma function / rank
 
Normal rank
Property / Symbols used: incomplete gamma function / qualifier
 
test:

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.m2addec
Property / Symbols used
 
Property / Symbols used: Q11323 / rank
 
Normal rank
Property / Symbols used: Q11323 / qualifier
 
test:

z 𝑧 {\displaystyle{\displaystyle z}}

z
Property / Symbols used: Q11323 / qualifier
 
xml-id: C8.S1.XMD2.m1odec
Property / Symbols used
 
Property / Symbols used: Q11324 / rank
 
Normal rank
Property / Symbols used: Q11324 / qualifier
 
test:

a 𝑎 {\displaystyle{\displaystyle a}}

a
Property / Symbols used: Q11324 / qualifier
 
xml-id: C8.S1.XMD3.m1odec
Property / Symbols used
 
Property / Symbols used: Q11329 / rank
 
Normal rank
Property / Symbols used: Q11329 / qualifier
 
test:

n 𝑛 {\displaystyle{\displaystyle n}}

n
Property / Symbols used: Q11329 / qualifier
 
xml-id: C8.S1.XMD6.m1gdec

Latest revision as of 12:49, 2 January 2020

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DLMF:8.8.E16
No description defined

    Statements

    test
    d n d z n ⁡ ( z - a ⁢ Γ ⁡ ( a , z ) ) = ( - 1 ) n ⁢ z - a - n ⁢ Γ ⁡ ( a + n , z ) , derivative 𝑧 𝑛 superscript 𝑧 𝑎 incomplete-Gamma 𝑎 𝑧 superscript 1 𝑛 superscript 𝑧 𝑎 𝑛 incomplete-Gamma 𝑎 𝑛 𝑧 {\displaystyle{\displaystyle\frac{{\mathrm{d}}^{n}}{{\mathrm{d}z}^{n}}(z^{-a}% \Gamma\left(a,z\right))=(-1)^{n}z^{-a-n}\Gamma\left(a+n,z\right),}}
    0 references
    DLMF id
    DLMF:8.8.E16
    0 references
    Symbols used
    derivative of $$f$$ with respect to $$x$$
    test
    d f d x derivative 𝑓 𝑥 {\displaystyle{\displaystyle\frac{\mathrm{d}\NVar{f}}{\mathrm{d}\NVar{x}}}}
    xml-id
    C1.S4.E4.m2abdec
    0 references
    incomplete gamma function
    test
    Γ ⁡ ( a , z ) incomplete-Gamma 𝑎 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{a},\NVar{z}\right)}}
    xml-id
    C8.S2.E2.m2addec
    0 references
    Q11323
    test
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C8.S1.XMD2.m1odec
    0 references
    Q11324
    test
    a 𝑎 {\displaystyle{\displaystyle a}}
    xml-id
    C8.S1.XMD3.m1odec
    0 references
    Q11329
    test
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C8.S1.XMD6.m1gdec
    0 references
     
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