DLMF:2.6.E33 (Q859): Difference between revisions

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Property / Symbols defined
 
Property / Symbols defined: fractional integral (locally) / rank
 
Normal rank
Property / constraint
 

μ > 0 𝜇 0 {\displaystyle{\displaystyle\mu>0}}

\mu>0
Property / constraint: μ > 0 𝜇 0 {\displaystyle{\displaystyle\mu>0}} / rank
 
Normal rank
Property / Symbols used
 
Property / Symbols used: gamma function / rank
 
Normal rank
Property / Symbols used: gamma function / qualifier
 
test:

Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}

\EulerGamma@{\NVar{z}}
Property / Symbols used: gamma function / qualifier
 
xml-id: C5.S2.E1.m2aadec
Property / Symbols used
 
Property / Symbols used: Q10770 / rank
 
Normal rank
Property / Symbols used: Q10770 / qualifier
 
test:

d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}

\diff{\NVar{x}}
Property / Symbols used: Q10770 / qualifier
 
xml-id: C1.S4.SS4.m1andec
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.m3andec
Property / Symbols used
 
Property / Symbols used: Q11028 / rank
 
Normal rank
Property / Symbols used: Q11028 / qualifier
 
test:

μ 𝜇 {\displaystyle{\displaystyle\mu}}

\mu
Property / Symbols used: Q11028 / qualifier
 
xml-id: C2.S6.XMD14.m1dec
Property / Symbols used
 
Property / Symbols used: Q11019 / rank
 
Normal rank
Property / Symbols used: Q11019 / qualifier
 
test:

f ⁢ ( t ) 𝑓 𝑡 {\displaystyle{\displaystyle f(t)}}

f(t)
Property / Symbols used: Q11019 / qualifier
 
xml-id: C2.S6.XMD2.m1ndec

Latest revision as of 16:14, 1 January 2020

No description defined
Language Label Description Also known as
English
DLMF:2.6.E33
No description defined

    Statements

    test
    I μ ⁢ f ⁢ ( x ) = 1 Γ ⁡ ( μ ) ⁢ ∫ 0 x ( x - t ) μ - 1 ⁢ f ⁢ ( t ) ⁢ d t , superscript 𝐼 𝜇 𝑓 𝑥 1 Euler-Gamma 𝜇 superscript subscript 0 𝑥 superscript 𝑥 𝑡 𝜇 1 𝑓 𝑡 𝑡 {\displaystyle{\displaystyle I^{\mu}f(x)=\frac{1}{\Gamma\left(\mu\right)}\int_% {0}^{x}(x-t)^{\mu-1}f(t)\mathrm{d}t,}}
    0 references
    DLMF id
    DLMF:2.6.E33
    0 references
    constraint
    μ > 0 𝜇 0 {\displaystyle{\displaystyle\mu>0}}
    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
    Q10770
    test
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1andec
    0 references
    Q10771
    test
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3andec
    0 references
    Q11028
    test
    μ 𝜇 {\displaystyle{\displaystyle\mu}}
    xml-id
    C2.S6.XMD14.m1dec
    0 references
    Q11019
    test
    f ⁢ ( t ) 𝑓 𝑡 {\displaystyle{\displaystyle f(t)}}
    xml-id
    C2.S6.XMD2.m1ndec
    0 references
     
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