Article contents
Franel integrals of order four
Published online by Cambridge University Press: 09 April 2009
Abstract
Let ((x)) = x −⌊x⌋−1/2 be the swatooth function. If a, b, c and e are positive integeral, then the integral or ((ax)) ((bx)) ((cx)) ((ex)) over the unit interval involves Apolstol's generalized Dedekind sums. By expressing this integral as a lattice-point sum we obtain an elementary method for its evaluation. We also give an elementary proof of the reciprocity law for the third generalized Dedekind sum.
MSC classification
- Type
- Research Article
- Information
- Copyright
- Copyright © Australian Mathematical Society 1996
References
- 3
- Cited by