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Sums of Products of Bernoulli Numbers
Abstract Closed expressions are obtained for sums of products of Bernoulli numbers of the form[formula], where the summation is extended over all nonnegative integers j 1 , …,  j N with j 1 + j 2 +…+Expand
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Some q-series identities related to divisor functions
  • K. Dilcher
  • Computer Science, Mathematics
  • Discret. Math.
  • 13 October 1995
The generating functions of the divisor functions σk(n) = Σd|ndk are expressed as sums of products of the series U m (q):= ∑ n=1 ∞ n m q n ∏ j=n+1 (1−q j ), m=1,…,k+1 , and vice versa. Expand
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Generalized Euler Constants for Arithmetical Progressions
The work of Lehmer and Briggs on Euler constants in arithmetical progressions is extended to the generalized Euler constants that arise in the Laurent expansion of g(s) about s = 1 . The results areExpand
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Roots of Independence Polynomials of Well Covered Graphs
Let G be a well covered graph, that is, all maximal independent sets of G have the same cardinality, and let ik denote the number of independent sets of cardinality k in G. We investigate the rootsExpand
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On generalized gamma functions related to the Laurent coefficients of the Riemann zeta function
SummaryWe study a class of generalized gamma functions Гk(z) which relate to the generalized Euler constantsγk (basically the Laurent coefficients ofζ(s)) as Г(z) does to the Euler constantγ. A newExpand
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Convolution identities and lacunary recurrences for Bernoulli numbers
Abstract We extend Euler's well-known quadratic recurrence relation for Bernoulli numbers, which can be written in symbolic notation as ( B 0 + B 0 ) n = − n B n − 1 − ( n − 1 ) B n , to obtainExpand
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We extend the Stern sequence, sometimes also called Stern's diatomic sequence, to polynomials with coefficients 0 and 1 and derive various properties, including a generating function. A simpleExpand
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Resultants and discriminants of Chebyshev and related polynomials
We show that the resultants with respect to x of certain linear forms in Chebyshev polynomials with argument x are again linear forms in Chebyshev polynomials. Their coefficients and arguments areExpand
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Shortened recurrence relations for Bernoulli numbers
We derive a number of general recurrence relations for Bernoulli numbers, as well as several known identities. Expand
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Higher-order convolutions for Bernoulli and Euler polynomials
Abstract We prove convolution identities of arbitrary orders for Bernoulli and Euler polynomials, i.e., sums of products of a fixed but arbitrary number of these polynomials. They differ from theExpand
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