Hypergeometric Double Sums Simplified

 

We present efficient methods for calculating linear recurrences of hypergeometric double sums and, more broadly, for multiple sums. This approach integrates the algorithmic theory of contiguous relations, ensuring its applicability to a wide range of input sums. Furthermore, we introduce novel techniques to enhance the core task of our method, which is computing rational solutions for parameterized linear recurrences. These advancements not only streamline calculations but also expand the toolkit for tackling complex mathematical problems involving hypergeometric series.

website: popularscientist.com

#HypergeometricSums

#MathematicalAlgorithms

#LinearRecurrences

#MultipleSums

#AlgorithmicTheory

#ContiguousRelations

#MathOptimization

#ParameterizedRecurrences

#ComputationalMathematics

#AdvancedSummation