DLMF:2.6.E38 (Q864): Difference between revisions

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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.m2acdec
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.m1cdec
Property / Symbols used
 
Property / Symbols used: convolution (locally) / rank
 
Normal rank
Property / Symbols used: convolution (locally) / qualifier
 
test:

{\displaystyle{\displaystyle\ast}}

\ast
Property / Symbols used: convolution (locally) / qualifier
 
xml-id: C2.S6.XMD17.m1ddec

Latest revision as of 16:15, 1 January 2020

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DLMF:2.6.E38
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    Statements

    t μ - 1 δ ( s - 1 ) = Γ ( μ ) Γ ( μ + 1 - s ) t μ - s , superscript 𝑡 𝜇 1 Dirac-delta 𝑠 1 Euler-Gamma 𝜇 Euler-Gamma 𝜇 1 𝑠 superscript 𝑡 𝜇 𝑠 {\displaystyle{\displaystyle t^{\mu-1}\ast{\delta^{(s-1)}}=\frac{\Gamma\left(% \mu\right)}{\Gamma\left(\mu+1-s\right)}t^{\mu-s},}}
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    t > 0 𝑡 0 {\displaystyle{\displaystyle t>0}}
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    δ ( x - a ) Dirac-delta 𝑥 𝑎 {\displaystyle{\displaystyle\delta\left(\NVar{x-a}\right)}}
    C1.S17.SS1.p1.m2acdec
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    Γ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    C5.S2.E1.m2acdec
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    μ 𝜇 {\displaystyle{\displaystyle\mu}}
    C2.S6.XMD14.m1cdec
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    {\displaystyle{\displaystyle\ast}}
    C2.S6.XMD17.m1ddec
    0 references