DLMF:2.11.E32 (Q1062): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q10754 / rank
 
Normal rank
Property / Symbols used: Q10754 / qualifier
 
test:

( m n ) binomial 𝑚 𝑛 {\displaystyle{\displaystyle\genfrac{(}{)}{0.0pt}{}{\NVar{m}}{\NVar{n}}}}

\binom{\NVar{m}}{\NVar{n}}
Property / Symbols used: Q10754 / qualifier
 
xml-id: C1.S2.SS1.m1adec
Property / Symbols used
 
Property / Symbols used: Q11145 / rank
 
Normal rank
Property / Symbols used: Q11145 / qualifier
 
test:

a n subscript 𝑎 𝑛 {\displaystyle{\displaystyle a_{n}}}

a_{n}
Property / Symbols used: Q11145 / qualifier
 
xml-id: C2.S11.XMD12.m1cdec
Property / Symbols used
 
Property / Symbols used: Q11146 / rank
 
Normal rank
Property / Symbols used: Q11146 / qualifier
 
test:

d n subscript 𝑑 𝑛 {\displaystyle{\displaystyle d_{n}}}

d_{n}
Property / Symbols used: Q11146 / qualifier
 
xml-id: C2.S11.XMD13.m1adec

Latest revision as of 16:43, 1 January 2020

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DLMF:2.11.E32
No description defined

    Statements

    test
    d n = ∑ j = 0 n ( - 1 ) j ⁢ ( n j ) ⁢ ( j + 1 ) n - 1 ⁢ s j a j + 1 ∑ j = 0 n ( - 1 ) j ⁢ ( n j ) ⁢ ( j + 1 ) n - 1 ⁢ 1 a j + 1 . subscript 𝑑 𝑛 superscript subscript 𝑗 0 𝑛 superscript 1 𝑗 binomial 𝑛 𝑗 superscript 𝑗 1 𝑛 1 subscript 𝑠 𝑗 subscript 𝑎 𝑗 1 superscript subscript 𝑗 0 𝑛 superscript 1 𝑗 binomial 𝑛 𝑗 superscript 𝑗 1 𝑛 1 1 subscript 𝑎 𝑗 1 {\displaystyle{\displaystyle d_{n}=\frac{\sum_{j=0}^{n}(-1)^{j}\genfrac{(}{)}{% 0.0pt}{}{n}{j}(j+1)^{n-1}\frac{s_{j}}{a_{j+1}}}{\sum_{j=0}^{n}(-1)^{j}\genfrac% {(}{)}{0.0pt}{}{n}{j}(j+1)^{n-1}\frac{1}{a_{j+1}}}.}}
    0 references
    DLMF id
    DLMF:2.11.E32
    0 references
    Symbols used
    Q10754
    test
    ( m n ) binomial 𝑚 𝑛 {\displaystyle{\displaystyle\genfrac{(}{)}{0.0pt}{}{\NVar{m}}{\NVar{n}}}}
    xml-id
    C1.S2.SS1.m1adec
    0 references
    Q11145
    test
    a n subscript 𝑎 𝑛 {\displaystyle{\displaystyle a_{n}}}
    xml-id
    C2.S11.XMD12.m1cdec
    0 references
    Q11146
    test
    d n subscript 𝑑 𝑛 {\displaystyle{\displaystyle d_{n}}}
    xml-id
    C2.S11.XMD13.m1adec
    0 references
     
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