GENERALIZATIONS OF BERNOULLI NUMBERS AND POLYNOMIALS

2003

47 citations recorded by the source corpus.

The concepts of Bernoulli numbers Bn, Bernoulli polynomials Bn(x), and the generalized Bernoulli numbers Bn(a, b) are generalized to the one Bn(x; a, b, c) which is called the generalized Bernoulli polynomials depending on three positive real parameters. Numerous properties of these polynomials and some relationships between Bn, Bn(x), Bn(a, b) ,a ndBn(x; a, b, c) are established.

Subfields: Algebra and Number Theory, Applied Mathematics, Atomic and Molecular Physics, and Optics

View Paper: https://www.semanticscholar.org/paper/cd9f3ca8dc733c0a3f8df4fffcbf6e12cbba7171

Citations in the corpus

• A new generalization of the Bernoulli and related polynomials (2010, unknown): “A remarkably great amount of research has been done on various generalizations and analogs of the Bernoulli polynomials and the Bernoulli numbers (see, for example, [5, 15, 18, 21, 23]).”
• Some Generalizations and Basic (or q-) Extensions of the Bernoulli, Euler (2011, unknown): “[51] was introduced and investigated recently by Srivastava et al.”
• Some families of Genocchi type polynomials and their interpolation functions (2012, unknown): “([33,34]; see also [6]) considered generalizations of the Bernoulli polynomials and the Euler polynomials depending on three real parameters.”
• Two closed forms for the Bernoulli polynomials (2015, unknown): “Hereafter, some papers such as [21,22] were published.”
• Generating functions for generalized Stirling type numbers, Array type polynomials, Eulerian type polynomials and their applications (2011, unknown): “([30]-[31], [24], [26], [35], [47], [49], [46], [48]).”