In this paper, by considering higher-order degenerate Bernoulli and Euler polynomials which were
introduced by Carlitz, we investigate some properties of mixed-type of those polynomials. In particular, we give
some identities of mixed-type degenerate special polynomials which are derived from the fermionic integrals on Zp
and the bosonic integrals on Zp.
term. By contrast, there is a surface term for the bosonic
[ p [ T,j. (20.18b)-dxd8= fn...1(x)
The ^-integral is analogous to a bosonicintegral always extended from
—oo to +00 for functions that vanish fast enough at infinity. There is
no concept of boundary of the ^-integration range.
486 Chapter Twenty
The purpose of this section is to investigate how (20.17) transforms
under changes of variables and to show that there is a natural measure
in any superphase space, the "Liouville measure."