Algebraic Transformations of Gauss Hypergeometric Functions

By Raimundas Vidunas. 2004

71 citations recorded by the source corpus.

This article gives a classification scheme of algebraic transformations of Gauss hypergeometric functions, or pull-back transformations between hypergeometric differential equations. The classification recovers the classical transformations of degree 2, 3, 4, 6, and finds other transformations of some special classes of the Gauss hypergeometric function. The other transformations are considered more thoroughly in a series of supplementing articles.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/0b4a90c6dcce2c7ea8b0bdf5805dfd95cb54ac8e

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. Mark van Hoeij
2. Holly Swisher
3. Raimundas Vidunas

In Computational Theory and Mathematics

1. Mark van Hoeij
2. Holly Swisher
3. Fang-Ting Tu
4. Raimundas Vidunas
5. Ling Long
6. Jenny G. Fuselier
7. Paul M. Terwilliger

In Statistical and Nonlinear Physics

1. Mark van Hoeij
2. Holly Swisher
3. Ling Long

Citations in the corpus

• Belyi functions for hyperbolic hypergeometric-to-Heun transformations (2012, background): “Definition 1.2 Given yet another positive integer n, a Belyi function ϕ : P1x → P1z is called (k, `,m)-minusn-regular if, with exactly n exceptions, all points above z = 1 have branching order k, all points above z = 0 have branching order `, and all points above z = ∞ have branching order m.”
• Hypergeometric Functions over Finite Fields (2015, background): “Yang’s first result is related to, by a Pfaff transformation, the first formula on page 165 of [92] by Vidūnas, which says”