DLMF:30.15.E7 (Q8949): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q10770 / rank
 
Normal rank
Property / Symbols used: Q10770 / qualifier
 
Defining formula:

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

\diff{\NVar{x}}
Property / Symbols used: Q10770 / qualifier
 
xml-id: C1.S4.SS4.m1acdec
Property / Symbols used
 
Property / Symbols used: Q10771 / rank
 
Normal rank
Property / Symbols used: Q10771 / qualifier
 
Defining formula:

∫ {\displaystyle{\displaystyle\int}}

\int
Property / Symbols used: Q10771 / qualifier
 
xml-id: C1.S4.SS4.m3acdec
Property / Symbols used
 
Property / Symbols used: Q12409 / rank
 
Normal rank
Property / Symbols used: Q12409 / qualifier
 
Defining formula:

n ≥ m 𝑛 𝑚 {\displaystyle{\displaystyle n\geq m}}

n\geq m
Property / Symbols used: Q12409 / qualifier
 
xml-id: C30.S1.XMD5.m1edec
Property / Symbols used
 
Property / Symbols used: Q12451 / rank
 
Normal rank
Property / Symbols used: Q12451 / qualifier
 
Defining formula:

τ > 0 𝜏 0 {\displaystyle{\displaystyle\tau>0}}

\tau>0
Property / Symbols used: Q12451 / qualifier
 
xml-id: C30.S15.XMD1.m1ddec
Property / Symbols used
 
Property / Symbols used: function (locally) / rank
 
Normal rank
Property / Symbols used: function (locally) / qualifier
 
Defining formula:

ϕ n ⁢ ( t ) subscript italic-ϕ 𝑛 𝑡 {\displaystyle{\displaystyle\phi_{n}(t)}}

\phi_{n}(t)
Property / Symbols used: function (locally) / qualifier
 
xml-id: C30.S15.XMD3.m1ddec
Property / Symbols used
 
Property / Symbols used: DLMF:30.15.E2 / rank
 
Normal rank
Property / Symbols used: DLMF:30.15.E2 / qualifier
 
Defining formula:

Λ Λ {\displaystyle{\displaystyle\Lambda}}

\Lambda
Property / Symbols used: DLMF:30.15.E2 / qualifier
 
xml-id: C30.S15.XMD4.m1edec

Latest revision as of 13:23, 2 January 2020

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DLMF:30.15.E7
No description defined

    Statements

    Defining formula
    ∫ - τ τ ϕ k ⁢ ( t ) ⁢ ϕ n ⁢ ( t ) ⁢ d t = Λ n ⁢ δ k , n , superscript subscript 𝜏 𝜏 subscript italic-ϕ 𝑘 𝑡 subscript italic-ϕ 𝑛 𝑡 𝑡 subscript Λ 𝑛 Kronecker 𝑘 𝑛 {\displaystyle{\displaystyle\int_{-\tau}^{\tau}\phi_{k}(t)\phi_{n}(t)\mathrm{d% }t=\Lambda_{n}\delta_{k,n},}}
    0 references
    DLMF id
    DLMF:30.15.E7
    0 references
    Symbols used
    Q10768
    Defining formula
    δ j , k Kronecker 𝑗 𝑘 {\displaystyle{\displaystyle\delta_{\NVar{j},\NVar{k}}}}
    xml-id
    introduction.Sx4.p1.t1.r4.m5adec
    0 references
    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1acdec
    0 references
    Q10771
    Defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3acdec
    0 references
    Q12409
    Defining formula
    n ≥ m 𝑛 𝑚 {\displaystyle{\displaystyle n\geq m}}
    xml-id
    C30.S1.XMD5.m1edec
    0 references
    Q12451
    Defining formula
    τ > 0 𝜏 0 {\displaystyle{\displaystyle\tau>0}}
    xml-id
    C30.S15.XMD1.m1ddec
    0 references
    function (locally)
    Defining formula
    ϕ n ⁢ ( t ) subscript italic-ϕ 𝑛 𝑡 {\displaystyle{\displaystyle\phi_{n}(t)}}
    xml-id
    C30.S15.XMD3.m1ddec
    0 references
    DLMF:30.15.E2
    Defining formula
    Λ Λ {\displaystyle{\displaystyle\Lambda}}
    xml-id
    C30.S15.XMD4.m1edec
    0 references
     
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