Direct Indefinite Summation

Zima, Eugene V.

doi:10.1145/2733693.2733715

ACM Commun. Comput. Algebra

2015

DOI: 10.1145/2733693.2733715

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Direct Indefinite Summation

Eugene V. Zima

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2019

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Accelerating indefinite hypergeometric summation algorithms

Zima

2019

ACM Commun. Comput. Algebra

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Let K be a field of characteristic zero, x an independent variable, E the shift operator with respect to x, i.e., Ef ( x ) = f ( x + 1) for an arbitrary f ( x ). Recall that a nonzero expression F ( x ) is called a hypergeometric term over K if there exists a rational function r ( x ) ∈ K( x ) such that F ( x + 1)/ F ( x ) = r ( x ). Usually r ( x ) is called the rational certificate of F ( x ). The problem of indefinite hypergeometric summation (anti-differencing) is: given a hypergeometric term F ( x ), find a hypergeometric term G ( x ) which satisfies the first order linear difference equation ( E − 1) G ( x ) = F ( x ). (1) If found, write Σ x F ( x ) = G ( x ) + c , where c is an arbitrary constant.

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Accelerating indefinite hypergeometric summation algorithms

Zima

2019

ACM Commun. Comput. Algebra

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Direct Indefinite Summation

Cited by 1 publication

References 9 publications

Accelerating indefinite hypergeometric summation algorithms

Accelerating indefinite hypergeometric summation algorithms

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