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Zbl 0768.11010
Butzer, P.L.; Hauss, M.; Leclerc, M.
Bernoulli numbers and polynomials of arbitrary complex indices. (English)
[J] Appl. Math. Lett. 5, No.6, 83-88 (1992). ISSN 0893-9659

For complex $\alpha$ with $\text{Re }\alpha > 1$ the authors define the Bernoulli periodic function ${\cal B}\sb \alpha(x)$ with period 1 by the Fourier series $${\cal B}\sb \alpha = -2\Gamma(\alpha + 1)\sum\sp \infty\sb{k=1}{\cos(2\pi kx - \alpha\pi/2)\over (2\pi k)\sp \alpha},$$ and study its connection with the classical Bernoulli polynomials and Bernoulli numbers.
[T.M.Apostol (Pasadena)]

MSC 2000:: *11B68 Bernoulli numbers, etc.

Keywords: Bernoulli periodic function; Fourier series; Bernoulli polynomials; Bernoulli numbers

Cited in: Zbl 0849.11021

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