New results of α-calculus

Abstract

We complete our basic presentation of the α-calculus. A generalized Stokes theorem is given. Several explicit calculations are done for analytic functions. We propose an extension of Fourier transform theory. We also give several complementary results.

Keywords:

• α-Calculus
• Bessel functions
• Analytic functions
• Stokes theorem
• Fourier analysis

Acknowledgements

The author was supported by Natural Sciences and Engineering Research Council of Canada, Grant OGP0009331.