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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
##### Keywords:
Euler polynomial; Bernoulli polynomial