Fractional Bernoulli and Euler Numbers and Related Fractional Polynomials—A Symmetry in Number Theory
Fractional Bernoulli and Euler Numbers and Related Fractional Polynomials—A Symmetry in Number Theory
Bernoulli and Euler numbers and polynomials are well known and find applications in various areas of mathematics, such as number theory, combinatorial mathematics, series expansions, and the theory of special functions. Using fractional exponential functions, we extend the classical Bernoulli and Euler numbers and polynomials to introduce their fractional-index-based types. …