DLMF:1.17.E23 (Q682): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: base of natural logarithm / rank
 
Normal rank
Property / Symbols used: base of natural logarithm / qualifier
 
test:

e {\displaystyle{\displaystyle\mathrm{e}}}

\expe
Property / Symbols used: base of natural logarithm / qualifier
 
xml-id: C4.S2.E11.m2aldec
Property / Symbols used
 
Property / Symbols used: Q10921 / rank
 
Normal rank
Property / Symbols used: Q10921 / qualifier
 
test:

L n ⁡ ( x ) = L n ( 0 ) ⁡ ( x ) shorthand-Laguerre-polynomial-L 𝑛 𝑥 Laguerre-polynomial-L 0 𝑛 𝑥 {\displaystyle{\displaystyle L_{\NVar{n}}\left(\NVar{x}\right)=L^{(0)}_{n}% \left(x\right)}}

\LaguerrepolyL[]{\NVar{n}}@{\NVar{x}}=\LaguerrepolyL[0]{n}@{x}
Property / Symbols used: Q10921 / qualifier
 
xml-id: C18.S1.I1.ix7.p1.m3adec
Property / Symbols used
 
Property / Symbols used: Q10756 / rank
 
Normal rank
Property / Symbols used: Q10756 / qualifier
 
test:

k 𝑘 {\displaystyle{\displaystyle k}}

k
Property / Symbols used: Q10756 / qualifier
 
xml-id: C1.S1.XMD4.m1edec

Latest revision as of 15:46, 1 January 2020

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DLMF:1.17.E23
No description defined

    Statements

    test
    δ ⁡ ( x - a ) = e - ( x + a ) / 2 ⁢ ∑ k = 0 ∞ L k ⁡ ( x ) ⁢ L k ⁡ ( a ) . Dirac-delta 𝑥 𝑎 superscript 𝑒 𝑥 𝑎 2 superscript subscript 𝑘 0 shorthand-Laguerre-polynomial-L 𝑘 𝑥 shorthand-Laguerre-polynomial-L 𝑘 𝑎 {\displaystyle{\displaystyle\delta\left(x-a\right)=e^{-(x+a)/2}\sum_{k=0}^{% \infty}L_{k}\left(x\right)L_{k}\left(a\right).}}
    0 references
    DLMF id
    DLMF:1.17.E23
    0 references
    Symbols used
    Q10915
    test
    δ ⁡ ( x - a ) Dirac-delta 𝑥 𝑎 {\displaystyle{\displaystyle\delta\left(\NVar{x-a}\right)}}
    xml-id
    C1.S17.SS1.p1.m2ajdec
    0 references
    base of natural logarithm
    test
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2aldec
    0 references
    Q10921
    test
    L n ⁡ ( x ) = L n ( 0 ) ⁡ ( x ) shorthand-Laguerre-polynomial-L 𝑛 𝑥 Laguerre-polynomial-L 0 𝑛 𝑥 {\displaystyle{\displaystyle L_{\NVar{n}}\left(\NVar{x}\right)=L^{(0)}_{n}% \left(x\right)}}
    xml-id
    C18.S1.I1.ix7.p1.m3adec
    0 references
    Q10756
    test
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C1.S1.XMD4.m1edec
    0 references
     
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