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A hybrid identity between Euler numbers and Bernoulli numbers. (Chinese. English summary) Zbl 1128.11308

Summary: Using the definitions of \(n\)th order Bernoulli and Euler numbers the authors obtain a hybrid identity for Bernoulli and Euler numbers of the form \[ B_n^{(k)}\left(\frac {k}{2}-\frac {k}{2^{l+1}}\right)=\frac {1}{4^n}\sum_{a=0}^n 2^aC_n^aB_a^{(k)}\left(\frac {k}{2}-\frac {k}{2^l}\right)E_{n-a}^{(k)}. \]

MSC:

11B68 Bernoulli and Euler numbers and polynomials
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