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Some identities on the Euler numbers arising from Euler basis polynomials. (English) Zbl 1289.05004
The authors prove that the first \(n\) Euler polynomials form a basis for the space of polynomials of degree at most \(n\). Using properties of Euler polynomials, they derive a number of identities valid on the products of Bernoulli and Euler polynomials.

MSC:
05A10 Factorials, binomial coefficients, combinatorial functions
05A15 Exact enumeration problems, generating functions
05E99 Algebraic combinatorics
11B68 Bernoulli and Euler numbers and polynomials
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