Abstract
The hypergeometric function is a slight generalization of the power fucntion. We will see this by the Schwarz map of the hypergeometric equation focussing on the behavior of this map when the local exponent-differences are purely imaginary
The author is grateful to the MPIM in Bonn and the JSPS.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
T. Ichikawa and M. Yoshida, On Schottky groups arising from the hypergeometric equation with imaginary exponents, Proc. AMS 132 (2003), 447–454.
T. Ichikawa and M. Yoshida, A family of Schottky groups arising from the hypergeometric equation, to appear in Proc. AMS.
K. Iwasaki, H. Kimura, S. Shimomura and M. Yoshida, From Gauss to Painlevé — A modern theory of special functions, Vieweg Verlag, Wiesbaden, 1991.
M. Kaneko and M. Yoshida, The kappa function, Internat. J. Math. 14 (2003), 1003–1013.
K. Matsumoto and M. Yoshida, Recent progress of interesection theory for twisted (co)homology groups, Advanced Studies in Pure Math. 27 (2000), 217–237.
T. Sasaki and M. Yoshida, A geometric study of the hypergeometric fucntion with imaginary exponents, Experimental Math. 10 (2000), 321–330.
F. Schilling, Beiträge sur geometrischen Theorie der Schwarzschen s-Funktion, Math. Annalen 44 (1894), 161–260.
F. Schilling, Die Geometrischen Theorie der Schwarzschen s-Funktion für komplexe Exponenten, Math. Annalen 46 (1895), 62–76, 529–538.
F. Schottky, Über eine specielle Function, welche bei einer bestimmten linearen Transformation ihres Arguments univerändert bleibt, J. Reine Angew. Math. 101 (1887) 227–272.
M. Yoshida, Fuchsian Differential Equations, Vieweg Verlag, 1987.
M. Yoshida, Hypergeometric Functions, My Love, Vieweg Verlag, 1997.
M. Yoshida, A naive-topological study of the contiguity relations of the hypergeometric function. To appear in Bedlewo Proceedings.
M. Zapf Abbildungseigenschaften allgemeiner Dreiecksfunktionen, Diplomarbeit der Universität Frankfurt, 1994.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2007 Birkhäuser Verlag Basel/Switzerland
About this chapter
Cite this chapter
Yoshida, M. (2007). From the Power Function to the Hypergeometric Function. In: Holzapfel, RP., Uludağ, A.M., Yoshida, M. (eds) Arithmetic and Geometry Around Hypergeometric Functions. Progress in Mathematics, vol 260. Birkhäuser Basel. https://doi.org/10.1007/978-3-7643-8284-1_14
Download citation
DOI: https://doi.org/10.1007/978-3-7643-8284-1_14
Publisher Name: Birkhäuser Basel
Print ISBN: 978-3-7643-8283-4
Online ISBN: 978-3-7643-8284-1
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)