DLMF:24.6.E6 (Q7470): 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.m1abdec

Revision as of 01:31, 2 January 2020

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DLMF:24.6.E6
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    E 2 n = k = 1 2 n ( - 1 ) k 2 k - 1 ( 2 n + 1 k + 1 ) j = 0 1 2 k - 1 2 ( k j ) ( k - 2 j ) 2 n . Euler-number-E 2 𝑛 superscript subscript 𝑘 1 2 𝑛 superscript 1 𝑘 superscript 2 𝑘 1 binomial 2 𝑛 1 𝑘 1 superscript subscript 𝑗 0 1 2 𝑘 1 2 binomial 𝑘 𝑗 superscript 𝑘 2 𝑗 2 𝑛 {\displaystyle{\displaystyle E_{2n}=\sum_{k=1}^{2n}\frac{(-1)^{k}}{2^{k-1}}{2n% +1\choose k+1}\*\sum_{j=0}^{\left\lfloor\tfrac{1}{2}k-\tfrac{1}{2}\right% \rfloor}{k\choose j}(k-2j)^{2n}.}}
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    DLMF:24.6.E6
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    E n Euler-number-E 𝑛 {\displaystyle{\displaystyle E_{\NVar{n}}}}
    C24.S2.SS2.m1abdec
    0 references