Abstract
We now turn to the relation between the Bernoulli polynomials and h-calculus. By Proposition 23.1, we have
or
where D1 is the h-derivative with h = 1 and ∝ f(x)d1x stands for the h-antiderivative with h=1. Applying the fundamental theorem of h-calculus (22.14), we have for a nonnegative integer n,
where a < band b - a ∈ ℤ. If we rewrite the right-hand side using (23.5) and let a = 0, b = M + 1, we get
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© 2002 Victor Kac.
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Kac, V., Cheung, P. (2002). Sums of Powers. In: Quantum Calculus. Universitext. Springer, New York, NY. https://doi.org/10.1007/978-1-4613-0071-7_24
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DOI: https://doi.org/10.1007/978-1-4613-0071-7_24
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