DLMF:2.6.E36 (Q862): Difference between revisions

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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.m1apdec
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.m3apdec
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.m1bdec
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.m1bdec

Latest revision as of 16:14, 1 January 2020

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DLMF:2.6.E36
No description defined

    Statements

    test
    ( t μ - 1 ∗ t - s - α ) ⁢ ( x ) = ∫ 0 x ( x - t ) μ - 1 ⁢ t - s - α ⁢ d t , ∗ superscript 𝑡 𝜇 1 superscript 𝑡 𝑠 𝛼 𝑥 superscript subscript 0 𝑥 superscript 𝑥 𝑡 𝜇 1 superscript 𝑡 𝑠 𝛼 𝑡 {\displaystyle{\displaystyle(t^{\mu-1}\ast t^{-s-\alpha})(x)=\int_{0}^{x}(x-t)% ^{\mu-1}t^{-s-\alpha}\mathrm{d}t,}}
    0 references
    DLMF id
    DLMF:2.6.E36
    0 references
    constraint
    s = 0 , 1 , 2 , … 𝑠 0 1 2 … {\displaystyle{\displaystyle s=0,1,2,\dots}}
    0 references
    Symbols used
    Q10770
    test
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1apdec
    0 references
    Q10771
    test
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3apdec
    0 references
    Q11028
    test
    μ 𝜇 {\displaystyle{\displaystyle\mu}}
    xml-id
    C2.S6.XMD14.m1bdec
    0 references
    convolution (locally)
    test
    ∗ ∗ {\displaystyle{\displaystyle\ast}}
    xml-id
    C2.S6.XMD17.m1bdec
    0 references
     
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