DLMF:24.14.E12 (Q7557): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q11238 / rank
 
Normal rank
Property / Symbols used: Q11238 / qualifier
 
Defining formula:

E n Euler-number-E 𝑛 {\displaystyle{\displaystyle E_{\NVar{n}}}}

\EulernumberE{\NVar{n}}
Property / Symbols used: Q11238 / qualifier
 
xml-id: C24.S2.SS2.m1acdec
Property / Symbols used
 
Property / Symbols used: Q10765 / rank
 
Normal rank
Property / Symbols used: Q10765 / qualifier
 
Defining formula:

det {\displaystyle{\displaystyle\det}}

\det
Property / Symbols used: Q10765 / qualifier
 
xml-id: C1.S3.SS1.m1aadec
Property / Symbols used
 
Property / Symbols used: Q10755 / rank
 
Normal rank
Property / Symbols used: Q10755 / qualifier
 
Defining formula:

! {\displaystyle{\displaystyle!}}

!
Property / Symbols used: Q10755 / qualifier
 
xml-id: introduction.Sx4.p1.t1.r15.m5aedec
Property / Symbols used
 
Property / Symbols used: Q12113 / rank
 
Normal rank
Property / Symbols used: Q12113 / qualifier
 
Defining formula:

k 𝑘 {\displaystyle{\displaystyle k}}

k
Property / Symbols used: Q12113 / qualifier
 
xml-id: C24.S1.XMD2.m1kdec
Property / Symbols used
 
Property / Symbols used: Q12110 / rank
 
Normal rank
Property / Symbols used: Q12110 / qualifier
 
Defining formula:

n 𝑛 {\displaystyle{\displaystyle n}}

n
Property / Symbols used: Q12110 / qualifier
 
xml-id: C24.S1.XMD5.m1kdec
Property / Symbols used
 
Property / Symbols used: Q12127 / rank
 
Normal rank
Property / Symbols used: Q12127 / qualifier
 
Defining formula:

r 𝑟 {\displaystyle{\displaystyle r}}

r
Property / Symbols used: Q12127 / qualifier
 
xml-id: C24.S14.XMD1.m1adec
Property / Symbols used
 
Property / Symbols used: Q12128 / rank
 
Normal rank
Property / Symbols used: Q12128 / qualifier
 
Defining formula:

s 𝑠 {\displaystyle{\displaystyle s}}

s
Property / Symbols used: Q12128 / qualifier
 
xml-id: C24.S14.XMD2.m1adec

Latest revision as of 01:47, 2 January 2020

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DLMF:24.14.E12
No description defined

    Statements

    Defining formula
    det ⁡ [ E r + s ] = ( - 1 ) n ⁢ ( n + 1 ) / 2 ⁢ ( ∏ k = 1 n k ! ) 2 . delimited-[] Euler-number-E 𝑟 𝑠 superscript 1 𝑛 𝑛 1 2 superscript superscript subscript product 𝑘 1 𝑛 𝑘 2 {\displaystyle{\displaystyle\det[E_{r+s}]=(-1)^{n(n+1)/2}\left(\prod_{k=1}^{n}% k!\right)^{2}.}}
    0 references
    DLMF id
    DLMF:24.14.E12
    0 references
    Symbols used
    Q11238
    Defining formula
    E n Euler-number-E 𝑛 {\displaystyle{\displaystyle E_{\NVar{n}}}}
    xml-id
    C24.S2.SS2.m1acdec
    0 references
    Q10765
    Defining formula
    det {\displaystyle{\displaystyle\det}}
    xml-id
    C1.S3.SS1.m1aadec
    0 references
    Q10755
    Defining formula
    ! {\displaystyle{\displaystyle!}}
    xml-id
    introduction.Sx4.p1.t1.r15.m5aedec
    0 references
    Q12113
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C24.S1.XMD2.m1kdec
    0 references
    Q12110
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C24.S1.XMD5.m1kdec
    0 references
    Q12127
    Defining formula
    r 𝑟 {\displaystyle{\displaystyle r}}
    xml-id
    C24.S14.XMD1.m1adec
    0 references
    Q12128
    Defining formula
    s 𝑠 {\displaystyle{\displaystyle s}}
    xml-id
    C24.S14.XMD2.m1adec
    0 references
     
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