DLMF:10.23.E13 (Q3467): Difference between revisions

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Property / constraint
 

n = 1 , 2 , … 𝑛 1 2 … {\displaystyle{\displaystyle n=1,2,\ldots}}

n=1,2,\dotsc
Property / constraint: n = 1 , 2 , … 𝑛 1 2 … {\displaystyle{\displaystyle n=1,2,\ldots}} / rank
 
Normal rank
Property / Symbols used
 
Property / Symbols used: Neumann’s polynomial / rank
 
Normal rank
Property / Symbols used: Neumann’s polynomial / qualifier
 
test:

O n ⁡ ( x ) Neumann-polynomial 𝑛 𝑥 {\displaystyle{\displaystyle O_{\NVar{n}}\left(\NVar{x}\right)}}

\NeumannpolyO{\NVar{n}}@{\NVar{x}}
Property / Symbols used: Neumann’s polynomial / qualifier
 
xml-id: C10.S23.E12.m2abdec
Property / Symbols used
 
Property / Symbols used: Q10755 / rank
 
Normal rank
Property / Symbols used: Q10755 / qualifier
 
test:

! {\displaystyle{\displaystyle!}}

!
Property / Symbols used: Q10755 / qualifier
 
xml-id: introduction.Sx4.p1.t1.r15.m5aadec
Property / Symbols used
 
Property / Symbols used: Q11169 / rank
 
Normal rank
Property / Symbols used: Q11169 / qualifier
 
test:

⌊ x ⌋ 𝑥 {\displaystyle{\displaystyle\left\lfloor\NVar{x}\right\rfloor}}

\floor{\NVar{x}}
Property / Symbols used: Q11169 / qualifier
 
xml-id: introduction.Sx4.p1.t1.r17.m4adec
Property / Symbols used
 
Property / Symbols used: Q11429 / rank
 
Normal rank
Property / Symbols used: Q11429 / qualifier
 
test:

n 𝑛 {\displaystyle{\displaystyle n}}

n
Property / Symbols used: Q11429 / qualifier
 
xml-id: C10.S1.XMD2.m1cdec
Property / Symbols used
 
Property / Symbols used: Q11428 / rank
 
Normal rank
Property / Symbols used: Q11428 / qualifier
 
test:

k 𝑘 {\displaystyle{\displaystyle k}}

k
Property / Symbols used: Q11428 / qualifier
 
xml-id: C10.S1.XMD3.m1kdec

Latest revision as of 12:31, 2 January 2020

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English
DLMF:10.23.E13
No description defined

    Statements

    test
    O n ⁡ ( t ) = 1 4 ⁢ ∑ k = 0 ⌊ n / 2 ⌋ ( n - k - 1 ) ! ⁢ n k ! ⁢ ( 2 t ) n - 2 ⁢ k + 1 , Neumann-polynomial 𝑛 𝑡 1 4 superscript subscript 𝑘 0 𝑛 2 𝑛 𝑘 1 𝑛 𝑘 superscript 2 𝑡 𝑛 2 𝑘 1 {\displaystyle{\displaystyle O_{n}\left(t\right)=\frac{1}{4}\sum_{k=0}^{\left% \lfloor n/2\right\rfloor}\frac{(n-k-1)!n}{k!}\left(\frac{2}{t}\right)^{n-2k+1}% ,}}
    0 references
    DLMF id
    DLMF:10.23.E13
    0 references
    constraint
    n = 1 , 2 , … 𝑛 1 2 … {\displaystyle{\displaystyle n=1,2,\ldots}}
    0 references
    Symbols used
    Neumann’s polynomial
    test
    O n ⁡ ( x ) Neumann-polynomial 𝑛 𝑥 {\displaystyle{\displaystyle O_{\NVar{n}}\left(\NVar{x}\right)}}
    xml-id
    C10.S23.E12.m2abdec
    0 references
    Q10755
    test
    ! {\displaystyle{\displaystyle!}}
    xml-id
    introduction.Sx4.p1.t1.r15.m5aadec
    0 references
    Q11169
    test
    ⌊ x ⌋ 𝑥 {\displaystyle{\displaystyle\left\lfloor\NVar{x}\right\rfloor}}
    xml-id
    introduction.Sx4.p1.t1.r17.m4adec
    0 references
    Q11429
    test
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C10.S1.XMD2.m1cdec
    0 references
    Q11428
    test
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C10.S1.XMD3.m1kdec
    0 references
     
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