Details:
Title  Algorithms for integrals of holonomic functions over domains defined by polynomial inequalities  Author(s)  Toshinori Oaku  Type  Article in Journal  Abstract  A holonomic function is a differentiable or generalized function which satisfies a holonomic system of linear partial or ordinary differential equations with polynomial coefficients. The main purpose of this paper is to present algorithms for computing a holonomic system for the definite integral of a holonomic function with parameters over a domain defined by polynomial inequalities. If the integrand satisfies a holonomic difference–differential system including parameters, then a holonomic difference–differential system for the integral can also be computed. In the algorithms, holonomic distributions (generalized functions in the sense of L. Schwartz) are inevitably involved even if the integrand is a usual function.  Keywords  Integration, Holonomic function, Dmodule, Generalized function, Gröbner basis  ISSN  07477171 
URL 
http://www.sciencedirect.com/science/article/pii/S0747717112000946 
Language  English  Journal  Journal of Symbolic Computation  Volume  50  Number  0  Pages  1  27  Year  2013  Edition  0  Translation 
No  Refereed 
No 
