Three Recitations on Holonomic Systems and Hypergeometric Series
نویسندگان
چکیده
منابع مشابه
Three Recitations on Holonomic Systems and Hypergeometric Series
When we teach calculus we have lectures and recitations. These notes are meant as “recitations” or something like “Schaum outlines” for the theory. The role of the “lectures” or “textbook” is provided by Gosper’s path-breaking paper “A Decision Procedure for Indefinite summation”, Proc. Nat. Acad. Sci. USA 75 (1978), 40-42, and by the following papers by myself and my collaborators, Gert Almkvi...
متن کاملPfaffian Systems of A-Hypergeometric Systems II - Holonomic Gradient Method
We give two efficient methods to derive Pfaffian systems for A-hypergeometric systems for the application to the holonomic gradient method for statistics. We utilize the Hilbert driven Buchberger algorithm and Macaulay type matrices in the two methods.
متن کاملElliptic Hypergeometric Series on Root Systems
We derive a number of summation and transformation formulas for elliptic hypergeometric series on the root systems An, Cn and Dn. In the special cases of classical and q-series, our approach leads to new elementary proofs of the corresponding identities.
متن کاملHolonomic Tools for Basic Hypergeometric Functions
With the exception of q-hypergeometric summation, the use of computer algebra packages implementing Zeilberger’s “holonomic systems approach” in a broader mathematical sense is less common in the field of q-series and basic hypergeometric functions. A major objective of this article is to popularize the usage of such tools also in these domains. Concrete case studies showing software in action ...
متن کاملThree Lectures on Hypergeometric Functions
In this course we will study multivariate hypergeometric functions in the sense of Gel’fand, Kapranov, and Zelevinsky (GKZ systems). These functions generalize the classical hypergeometric functions of Gauss, Horn, Appell, and Lauricella. We will emphasize the algebraic methods of Saito, Sturmfels, and Takayama to construct hypergeometric series and the connection with deformation techniques in...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Symbolic Computation
سال: 1995
ISSN: 0747-7171
DOI: 10.1006/jsco.1995.1072