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Convolution and Reciprocity Formulas for Bernoulli Polynomials
-
Takashi Agoh
and
Karl Dilcher
Published/Copyright:
August 4, 2011
Abstract
We prove a new convolution identity for sums of products of two Bernoulli polynomials. This can be rewritten to obtain a reciprocity relation for a related sum. The proof uses some results on Stirling numbers of both kinds which are of independent interest. In particular, a class of polynomials related to the Stirling numbers of the second kind turns out to be a useful tool.
Keywords.: Bernoulli Numbers; Bernoulli Polynomials; Stirling Numbers; Convolutions; Reciprocity Relations
Received: 2010-10-07
Accepted: 2011-05-18
Published Online: 2011-08-04
Published in Print: 2011-December
© de Gruyter 2011
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Keywords for this article
Bernoulli Numbers;
Bernoulli Polynomials;
Stirling Numbers;
Convolutions;
Reciprocity Relations
Articles in the same Issue
- Completely Multiplicative Automatic Functions
- The k-Periodic Fibonacci Sequence and an Extended Binet's Formula
- Robin's Theorem, Primes, and a New Elementary Reformulation of the Riemann Hypothesis
- Reducing the Erdős–Moser Equation 1n + 2n + ⋯ + kn = (k + 1)n Modulo k and k2
- On Some Conjectures Concerning Stern's Sequence and Its Twist
- Number of Weighted Subsequence Sums with Weights in {1, –1}
- Binomial Coefficient – Harmonic Sum Identities Associated to Supercongruences
- Euler's Pentagonal Number Theorem Implies the Jacobi Triple Product Identity
- On Directions Determined by Subsets of Vector Spaces over Finite Fields
- A Remark on a Paper of Luca and Walsh
- On the Tennis Ball Problem
- On the Conditioned Binomial Coefficients
- Convolution and Reciprocity Formulas for Bernoulli Polynomials
- Counting Finite Languages by Total Word Length
