A B-spline approach to [formula omitted]-Eulerian polynomials

Abstract

We present q-analogues of exponential Euler polynomials and Euler–Frobenius polynomials from B-splines with knots both at q-integers and in geometric progression. We also investigate the relations between q-Eulerian numbers, q-Eulerian polynomials, q-Euler–Frobenius polynomials and B-splines. We derive q-Euler–Frobenius polynomials using q-analogue of exponential splines. It is shown that B-splines with knots at q-integers and B-splines with knots in geometric progression have same values on their knot points. We also construct a q-analogue of Worpitzky identity.