#### Abstract

Here presented is the interrelationship between Eulerian polynomials, Eulerian fractions and Euler-Frobenius polynomials, Euler-Frobenius fractions, B-splines, respectively. The properties of Eulerian polynomials and Eulerian fractions and their applications in B-spline interpolation and evaluation of Riemann-zeta function values at odd integers are given. The relation between Eulerian numbers and B-spline values at knot points are also discussed.

#### Disciplines

Applied Mathematics | Mathematics

#### Recommended Citation

He, Tian-Xiao, "Eulerian Polynomials and B-Splines" (2012). *Scholarship*. 52.

http://digitalcommons.iwu.edu/math_scholarship/52

## Comments

The

Journal of Computational and Applied Mathematicsis published by Elsevier, http://www.journals.elsevier.com/journal-of-computational-and-applied-mathematics/.