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Relationships between generalized Bernoulli numbers and polynomials and generalized Euler numbers and polynomials. (English) Zbl 1042.11012
Let \(a,b,c\) be positive numbers. The generalized Bernoulli and Euler numbers are defined via the generating functions \(\frac{t}{b^t-a^t}\) and \(\frac{2c^t}{b^{2t}+a^{2t}}\) respectively, so that the classical sequences are obtained if \(a=1\), \(b=c=e\). A generalization of the Bernoulli and Euler polynomials is introduced in a similar way. The authors prove several identities containing the above sequences.

MSC:
11B68 Bernoulli and Euler numbers and polynomials
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