1,307 research outputs found
Generalized Bernoulli numbers and a formula of Lucas
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
Interpolation function of the genocchi type polynomials
The main purpose of this paper is to construct not only generating functions
of the new approach Genocchi type numbers and polynomials but also
interpolation function of these numbers and polynomials which are related to a,
b, c arbitrary positive real parameters. We prove multiplication theorem of
these polynomials. Furthermore, we give some identities and applications
associated with these numbers, polynomials and their interpolation functions.Comment: 14 page
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