About the limiting cases of the Riemann function
Authors:
Abstract
Let us investigate the limiting cases of the Riemann function. Let us take the differential equation of the P function and examine the functions (see the article). Following Riemann's example, we imagine the path of integration as a flexible, stretchable and easily movable thread. In its motion, a special point deforms this path, pushing it ahead and never crossing it. With this representation of the integration path, from closed curves corresponding to integrals (11), (13), (15), for integrals (16), (18), (20) we obtain open paths in certain directions extending to infinity.
Область исследования:
(Archived) Articles
Funding:
None
References
- F. Klein. Lecture on the hypergeometric function.
- R. Olbricht. Studies on spherical and cylindrical functions. (Acta Leopoldina, 52).
- F. Schilling. Contributions to the geometric theory of Schwarz's s-Function (Mathematische Annalen, 44).