DLMF:2.6.E13 (Q838): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q10759 / rank
 
Normal rank
Property / Symbols used: Q10759 / qualifier
 
test:

( a ) n Pochhammer 𝑎 𝑛 {\displaystyle{\displaystyle{\left(\NVar{a}\right)_{\NVar{n}}}}}

\Pochhammersym{\NVar{a}}{\NVar{n}}
Property / Symbols used: Q10759 / qualifier
 
xml-id: C5.S2.SS3.m1adec
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.m1agdec
Property / Symbols used
 
Property / Symbols used: Q10905 / rank
 
Normal rank
Property / Symbols used: Q10905 / qualifier
 
test:

⟨ Λ , ϕ ⟩ distribution Λ italic-ϕ {\displaystyle{\displaystyle\left\langle\NVar{\Lambda},\NVar{\phi}\right% \rangle}}

\intinnerprod{\NVar{\Lambda}}{\NVar{\phi}}
Property / Symbols used: Q10905 / qualifier
 
xml-id: C1.S16.SS1.p5.m5abdec
Property / Symbols used
 
Property / Symbols used: Q10784 / rank
 
Normal rank
Property / Symbols used: Q10784 / qualifier
 
test:

∈ {\displaystyle{\displaystyle\in}}

\in
Property / Symbols used: Q10784 / qualifier
 
xml-id: introduction.Sx4.p1.t1.r10.m2abdec
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.m3agdec
Property / Symbols used
 
Property / Symbols used: Q11023 / rank
 
Normal rank
Property / Symbols used: Q11023 / qualifier
 
test:

𝒯 𝒯 {\displaystyle{\displaystyle\mathcal{T}}}

\mathcal{T}
Property / Symbols used: Q11023 / qualifier
 
xml-id: C2.S6.XMD6.m1bdec

Latest revision as of 16:11, 1 January 2020

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DLMF:2.6.E13
No description defined

    Statements

    test
    ⟨ t - s - α , ϕ ⟩ = 1 ( α ) s ⁢ ∫ 0 ∞ t - α ⁢ ϕ ( s ) ⁢ ( t ) ⁢ d t , distribution superscript 𝑡 𝑠 𝛼 italic-ϕ 1 Pochhammer 𝛼 𝑠 superscript subscript 0 superscript 𝑡 𝛼 superscript italic-ϕ 𝑠 𝑡 𝑡 {\displaystyle{\displaystyle\left\langle t^{-s-\alpha},\phi\right\rangle=\frac% {1}{{\left(\alpha\right)_{s}}}\int_{0}^{\infty}t^{-\alpha}\phi^{(s)}(t)\mathrm% {d}t,}}
    0 references
    DLMF id
    DLMF:2.6.E13
    0 references
    constraint
    ϕ ∈ 𝒯 italic-ϕ 𝒯 {\displaystyle{\displaystyle\phi\in\mathcal{T}}}
    0 references
    Symbols used
    Q10759
    test
    ( a ) n Pochhammer 𝑎 𝑛 {\displaystyle{\displaystyle{\left(\NVar{a}\right)_{\NVar{n}}}}}
    xml-id
    C5.S2.SS3.m1adec
    0 references
    Q10770
    test
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1agdec
    0 references
    Q10905
    test
    ⟨ Λ , ϕ ⟩ distribution Λ italic-ϕ {\displaystyle{\displaystyle\left\langle\NVar{\Lambda},\NVar{\phi}\right% \rangle}}
    xml-id
    C1.S16.SS1.p5.m5abdec
    0 references
    Q10784
    test
    ∈ {\displaystyle{\displaystyle\in}}
    xml-id
    introduction.Sx4.p1.t1.r10.m2abdec
    0 references
    Q10771
    test
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3agdec
    0 references
    Q11023
    test
    𝒯 𝒯 {\displaystyle{\displaystyle\mathcal{T}}}
    xml-id
    C2.S6.XMD6.m1bdec
    0 references
     
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