# Über die Lösung algebraischer Gleichungssysteme durch hypergeometrische Funktionen

@article{Mayr1936berDL, title={{\"U}ber die L{\"o}sung algebraischer Gleichungssysteme durch hypergeometrische Funktionen}, author={Karl Mayr}, journal={Monatshefte f{\"u}r Mathematik und Physik}, year={1936}, volume={45}, pages={280-313} }

## 23 Citations

### A partial factorization of the powersum formula

- MathematicsInt. J. Math. Math. Sci.
- 2004

This work will use the Ahypergeometric linear partial differential equations of Mayr and Gelfand to find a particular factor of some terms of this α-resolvent of P and demonstrate this factorization on an α- Resolvent for quadratic and cubic polynomials.

### On Taylor series of zeros with general base function

- Mathematics
- 2021

We prove a formula for the Taylor series coefficients of a zero of the sum of a complex-exponent polynomial and a base function which is a general holomorphic function with a simple zero. Such a…

### Holonomic functions and prehomogeneous spaces

- Mathematics
- 2021

A function that is analytic on a domain of C is holonomic if it is the solution to a holonomic system of linear homogeneous differential equations with polynomial coefficients. We define and study…

### On Taylor series of zeros of complex-exponent polynomials

- Mathematics
- 2021

We prove a factorization formula for the Taylor series coefficients of a zero of a polynomial as a function of the polynomial’s coefficients. This result extends to more general functions which we…

### A generalized hypergeometric system

- Mathematics
- 2013

We give a combinatorial formula of the dimension of global solutions to a generalization of Gauss-Aomoto-Gelfand hyperge- ometric system, where the quadratic differential operators are replaced by…

### Heteroscedastic Analysis in Nonlinear Modeling

- Mathematics
- 2013

In order to discuss nonlinear, it is necessary to know linear regressive as a priori. Without simple regression as the starting point, it would be difficult to understand nonlinear regression. In…

### Hypergeometric functions and binomials

- Mathematics
- 2008

We highlight the role of primary decomposition of binomial ideals in a commutative polynomial ring, in the description of the holonomicity, the holonomic rank, and the shape of solutions of…

### A G ] 1 4 N ov 2 00 5 GKZ Hypergeometric Structures

- Mathematics
- 2008

This text is based on lectures by the author in the Summer School Algebraic Geometry and Hypergeometric Functions in Istanbul in June 2005. It gives a review of some of the basic aspects of the…

### Bases in the solution space of the Mellin system

- Mathematics
- 2007

We consider algebraic functions satisfying equations of the following form: (1) Here , , and is a function of the complex variables . Solutions of such algebraic equations are known to satisfy…