and applications. (English) Zbl 0849.11021
Anastassiou, George (ed.) et al., Approximation, probability, and related fields. Proceedings of a conference, Santa Barbara, CA, USA, May 20-22, 1993. New York, NY: Plenum. 127-150 (1994).
In an earlier paper [Appl. Math. Lett. 5, No. 6, 83-88 (1992; Zbl 0768.11010
)], the first and last authors, along with M. Leclerc
, introduced Bernoulli numbers and Bernoulli polynomials with arbitrary complex indices. This paper uses a different method to extend the classical Euler polynomials
in which both the index
and the argument
are complex numbers. The key idea is to define
by a contour integral taken along a loop around the negative real axis. Many interesting applications are given.
|11B68||Bernoulli and Euler numbers and polynomials|