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Generalized Bernoulli numbers and a formula of Lucas

Abstract : An overlooked formula of E. Lucas for the generalized Bernoulli numbers is proved using generating functions. This is then used to provide a new proof and a new form of a sum involving classical Bernoulli numbers studied by K. Dilcher. The value of this sum is then given in terms of the Meixner-Pollaczek polynomials.
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  • HAL Id : hal-01322848, version 1
  • ARXIV : 1402.2993

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Victor H. Moll, Christophe Vignat. Generalized Bernoulli numbers and a formula of Lucas. The Fibonacci Quarterly, Dalhousie University, 2015, 53 (4), pp.349. ⟨hal-01322848⟩

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